  We study the validity of a relation by Drell, Levy and Yan (DLY) connecting
the deep inelastic structure (DIS) functions and the single-particle
fragmentation functions in e^+e^- annihilation which are defined in the
spacelike (q^2<0) and timelike (q^2>0) regions respectively. Here q denotes the
momentum of the virtual photon exchanged in the deep inelastic scattering
process or the annihilation process. An extension of the DLY-relation, which
originally was only derived in the scaling parton model, to all orders in QCD
leads to a connection between the two evolution kernels determining the
q^2-dependence of the DIS structure functions and the fragmentation functions
respectively. In relation to this we derive the transformation relations
between the space-and time-like splitting functions up to next-to-leading order
(NLO) and the coefficient functions up to NNLO both for unpolarized and
polarized scattering. It is shown that the evolution kernels describing the
combined singlet evolution for the structure functions F_2(x,Q^2), F_L(x,Q^2)
where Q^2=|q^2| or $F_2(x,Q^2), \partial F_2(x,Q^2)/\partial \ln(Q^2)$ and the
corresponding fragmentation functions satisfy the DLY relation up to
next-to-leading order. We also comment on a relation proposed by Gribov and
Lipatov.
