  For solution $u(x,t)$ to degenearte parabolic equations in a bounded domain
$\Omega$ with homogenous boundary condition, we consider backward problems in
time: determine $u(\cdot,t_0)$ in $\Omega$ by $u(\cdot,T)$, where $t$ is the
time variable and $0\le t_0 < T$. Our main results are conditional stability
under boundedness assumptions on $u(\cdot,0)$. The proof is based on a weighted
$L^2$-estimate of $u$ whose weight depends only on $t$, which is an inequality
of Carleman's type. Moreover our method is applied to semilinear degenerate
parabolic equations.
