  The contributions to non-singlet evolution kernels $P(z)$ for the DGLAP
equation and $V(x,y)$ for the Brodsky-Lepage evolution equation are calculated
for certain classes of diagrams which include the renormalon chains. Closed
expressions are obtained for the sums of contributions associated with these
diagram classes. Calculations are performed in the $[\phi^3]_6$ model and QCD
in the \MSbar scheme. The contribution for one of the classes of diagrams
dominates for a number of flavors $N_f \gg 1$. For the latter case, a simple
solution to the Brodsky-Lepage evolution equation is obtained.
