  We obtain sufficient conditions ensuring the existence of a uniformly
continuous and H\"older continuous homeomorphism between the solutions of a
linear system of differential equations with piecewise constant argument of
generalized type and the solutions of the quasilinear corresponding system. We
use a definition (recently introduced by M. Akhmet) of exponential dichotomy
for those systems combined with technical assumptions on the nonlinear part.
Our result generalizes a previous work of G. Papaschinopoulos.
