  We prove the finite time blow-up for $C^1$ solutions to the Euler-Poisson
equations in $\Bbb R^n$, $n\geq 1$, with/without background density for initial
data satisfying suitable conditions. We also find a sufficient condition for
the initial data such that $C^3$ solution breaks down in finite time for the
compressible Euler equations for polytropic gas flows.
