  We consider a nonautonomous system \[ \dot x=A(t)x+f(t,x,y),\quad \dot y =
g(t,y)\] and give conditions under which there is a transformation of the form
$H(t,x,y)=(x+h(t,x,y),y)$ taking its solutions onto the solutions of the
partially linearized system \[ \dot x=A(t)x,\quad \dot y = g(t,y).\] Shi and
Xiong \cite{SX} proved a special case where $g(t,y)$ was a linear function of
$y$ and $\dot x=A(t)x$ had an exponential dichotomy. Our assumptions on $A$ and
$f$ are of the general form considered by Reinfelds and Steinberga \cite{RS},
which include many of the generalizations of Palmer's theorem proved by other
authors. Inspired by the work of Shi and Xiong, we also prove H\" older
continuity of $H$ and its inverse in $x$ and $y$. Again the proofs are given in
the context of Reinfelds and Steinberga but we show what the results reduce to
when $\dot x=A(t)x$ is assumed to have an exponential dichotomy. The paper is
concluded with the discrete version of the results.
