  We extract the small x asymptotic behaviour of the Altarelli-Parisi splitting
functions from their expansion in leading logarithms of 1/x. We show in
particular that the nominally next-to-leading correction extracted from the
Fadin-Lipatov kernel is enhanced asymptotically by an extra ln 1\x over the
leading order. We discuss the origin of this problem, its dependence on the
choice of factorization scheme, and its all-order generalization. We derive
necessary conditions which must be fulfilled in order to obtain a well behaved
perturbative expansion, and show that they may be satisfied by a suitable
reorganization of the original series.
