There is no hard endpoint to the Acheulean; its tool types -- in particular the handaxe -- last well into the MSA/Middle Paleolithic. Here are some notes on the later occurrences in Africa:
Sheppard and Kleindienst (1996) considered the technological changes from ESA to MSA at Kalambo Falls, finding:
...there is little change, at this site, in the basic techniques of blank production or the attributes of the blanks produced from the ESA to the MSA. The only marked change to occur is the loss of large cutting tools (hand axes, cleavers) and their replacement by heavy-duty forms (core axes, picks). It is hypothesized that this change marks a decline in portability as a factor in the design of large edge tools (Sheppard and Kleindienst 1996:171).
McBrearty (2003) reflects on the late persistence of characteristic Acheulean handaxes in association with some of the earliest fossils of "modern" humans, the Herto hominids from the Middle Awash of Ethiopia:
At 160-154 ka, the Herto handaxes are the latest survivors of Acheulean technology known in Africa. Formerly, the best candidates were those from the site of Rooidam, South Africa, where a U-series date indicated they might date to ~ 170 ka (Szabo and Butzer 1979). K/Ar dates of ~ 240 ka for Acheulean artifacts from the Kapthurin Formation, Kenya (Leakey et al. 1969, Tallon 1978) have frequently been cited as the date for terminal Acheulean in east Africa, but new more precise 40Ar/39Ar dating now shows these to predate 285 ka (Deino and McBrearty 2002).
What does the presence of Acheulean tools at 160 ka signify? The nature of archaeological change in the African Middle Pleistocene is murky, but the most obvious development is the abandonment of Acheulean technology, usually thought to have been made by H. erectus and its replacement by implements of MSA traditions, believed to have been produced by H. sapiens. In a nutshell, this comprises the replacement of handaxes and cleavers by points, signifying a shift from hand-held to hafted tools, and the birth of projectile technology. The presence of Levallois technology is usually considered to be a feature of the MSA, but it is present in late Acheulean contexts as well. In fact, the big flakes used to make African late Acheulean handaxes, including some Herto and Kapthurin specimens, may be struck from Levallois cores....The earliest MSA points were once thought to be those from Gademotta, Ethiopia, dated by K/Ar to 235 ka (Wendorf et al. 1994). Retouched points from the Kapthurin Formation predate those from Gademotta by 50,000 years. Dated by 40/Ar/39Ar to > 285 ka (Deino and McBrearty 2002), the are currently the oldest in Africa. A similar date is estimated for the basal MSA at Florisbad, South Africa (Grün et al. 1996), though these levels have not yet yielded points (Kuman and Clarke 1986, Kuman et al. 1999). Both retouched points and Levallois points have been recovered at Twin Rivers, Zambia, where they are dated by U-series to 265 ka (Barham 2000) (McBrearty 2003:1-2).
McBrearty briefly discusses two alterative hypotheses. One is that the Acheulean handaxes are markers of a biological species, and that MSA points and other artifacts were made by some other species, or multiple species. The problems with this hypothesis are manifold, including the association of the handaxes with fossil remains that would be uncomfortable fits in H. erectus at best. Yet, the hypothesis can be sustained by the additional assumption that multiple species cooccupied the same African paleolandscapes with sufficient contemporaneity to drop their tools in the same places:
Or can the archaeological record of the African Middle Pleistocene represent the behaviour of several species? Might different tools be the distinctive signatures of different populations or species who are competing with each other for the same territory and resources? A similar scenario of interspecific competition seems to have been played out between H. sapiens and the Neanderthals in Europe after 40 ka, but there the replacement was complete within 10,000 years or so. Africa is a far more enormous continent than Europe, its Pleistocene population far less dense, and our knowledge of its record less finely resolved. The 125,000 years represented by the Acheulean to Middle Stone Age transition in Africa is more than four times greater than the entire timespan of the residence of H. sapiens in Europe, but only a handful of African sites from this long time period have yet been explored.
The other hypothesis is that the handaxe appears wherever it is functionally relevant, regardless of phylogeny. Acheulean elements may have been independently invented again and again:
Archaeologists routinely stress the uniformity of the Acheulean tradition, and rarely entertain the possibility that the category 'handaxe' is an artificial construct that we impose upon the material. Experimental work by Jones (1994) shows that the familiar tear-drop shape of the handaxe is a design compromise resulting from attempts to gain the maximum cutting edge from the minimum weight of stone. The same techniques of blank production and bifacial retouch were employed in many cases to make both Acheulean handaxes and MSA points, and in the Kapthurin Formation the two classes of artefacts can grade into each other. Furthermore the tear drop shape occurs repeatedly in the archaeological record in cases where there is no evidence of 'phylogenetic' relation. Many projectile points from Africa, Europe, the Near East, and even the New World have similar plan forms (McBrearty 2001; Otte 2003), but there is clearly no 'phylogenetic' relationship among them. Rather, the recurrence of this target form demonstrates the design constraints inherent in fractured stone, and it appears to have been rediscovered repeatedly by tool makers in the course of prehistory (McBrearty 2003:2-3).
Of course, if the recurrence of the handaxe across the 1.4 million years of the Acheulean resulted from its function rather than a continuous chain cultural transmission, then it takes away one of the principal pieces of evidence that Acheulean people had any substantive culture at all.
As far as handaxes are concerned, that may be a good thing. The maintenance of a single cultural tradition across much of three continents over a million years by exclusively social transmission seems incredible. Some have suggested that the handaxe is hardwired into the human genome, a proposition that seems even less credible (at least, to me). Absent these means of transmission, we are left with the proposition that the handaxe did not fade from the earth because of its functional utility -- either it was the tool that did the job the best, or it was the best tool that humans were capable of making that did the job adequately. If function and human ability combined to make it so persistent, it should not be the least bit surprising that the form should recur in later contexts -- in the scenario of recurrent invention, it never really went away. The production of handaxes on large Levallois flakes seems especially relevant.
One view of the uniformity of handaxe variation across space is that humans maintained strong cultural links across large distances. The knowledge of handaxe production and the concept of handaxe shape were highly conserved cultural markers that were widely spread.
But the alternative hypothesis, that handaxe form was repeatedly invented by hominids and actually served as the best possible tool given its purpose and hominid flaking capacities, does not require long-distance cultural interactions to maintain the uniformity of the tradition. Nor does it require the recurrent movement of people over vast distances to spread the information. Given the lack of evidence for such long-distance movement, this hypothesis gains a bit of credibility.
Raw material utilization in the Acheulean is highly localized. People may have been using the large tools as repositories for further flaking, and they may have curated them for some time. But they did not transport them over vast distances. Ordinarily, Acheulean people do not appear to have transported material over distances greater than the possible daily movement of a single individual -- a few tens of kilometers.
It raises an obvious question: Is high mobility (in other words, hunter-gatherer-like mobility) a shibboleth of the assumption that handaxe form required culture? Did earlier humans actually have very small, limited home ranges and daily movement patterns? After all, if humans carried handaxes around for their utility, and they didn't manufacture a new one every day, then some handaxes ought to represent week-long movements or even longer.
Sheppard PJ, Kleindienst MR. 1996. Technological change in the Earlier and Middle Stone Age of Kalambo Falls (Zambia). Afr Archaeol Rev 13:171-196. DOI link
McBrearty S. 2003. Patterns of technological change at the origin of Homo sapiens. Before Farming 3:1-6.