Nonautonomous parabolic equations of the form $u_t - \Delta u = f(u,t)$
on a symmetric domain is considered. Using the moving-hyperplane
method it is proved that any bounded nonnegative solution  symmetrizes
as $t \rightarrow  \infty$.  This is a parabolic analog of a well-known
symmetry result of Gidas,  Ni and Nirenberg for elliptic equations.