  The purpose of this note is to extend the recent generalized version of the
Grobman-Hartman theorem established by Bernardes Jr. and Messaoudi from an
autonomous to the nonautonomous dynamics. More precisely, we prove that any
sufficiently small perturbation of a nonautonomous linear dynamics that admits
a generalized exponential dichotomy is topologically conjugated to its linear
part. In addition, we prove that under certain mild additional conditions, the
conjugacy is in fact H\"older continuous.
