A number of questions concerning the evolution and the function of the alpha satellite DNA sequences present at the centromere of all human chromosomes are still open. In this paper, we present data which could contribute to understanding these points. It is shown here that the alphoid sequences within which L1 elements are found are quite divergent from those of the homogeneous alphoid subsets present at each centromere where none has so far been detected. In addition, a number of L1s are detected close to the ends of the alpha satellite blocks. A fairly high proportion exhibit a polymorphism of presence/absence. Strikingly, several L1s localized at a distance from each other are always either present or absent simultaneously. This is interpreted as resulting from intrachromosomal recombination, through distant L1s, leading to deletion of several of them at once together with their surrounding alphoid sequences. The parameters determining which portion of the several megabases of alphoid sequences is actually involved in the centromeric function are not known. From the above data we suggest that the alpha satellite domain within which DNA sequences are recruited to form a centromere is both homogeneous in sequence and uninterrupted by L1s or any other retrotransposons. Conversely, non-centromere competent alphoid sequences would be both divergent and punctuated by scattered L1 elements, particularly at the borders of the alphoid blocks. On the grounds of these data and hypotheses, a model is presented in which it is postulated that accumulation of L1 insertions within a centromere competent alphoid domain is ruining this competence, the consequence being damage to or even loss of the centromere-forming capability of the chromosome. Restoration of fully centromere-forming competence is supposed to occur by two alternative means, either de-novo amplification of a homogeneous and uninterrupted alphoid domain or by unequal crossing over with a homologue harbouring a large competent one. If L1 retrotransposons are acting detrimentally to centromere integrity (for the worst), one must also consider them as having positive consequences on chromosomes by preventing their centromeres from swelling indefinitely by the addition of alphoid sequences (for the best). The data and ideas presented here fit well with those already put forward by Csink and Henikoff (1998) using the example of Drosophila.