  The Fujita phenomenon for nonlinear parabolic problems $\partial tu = \Delta
u + up$ in an exterior domain of RN under the dynamical boundary conditions is
investigated in the superlinear case. As in the case of Dirichlet boundary
conditions, it turns out that there exists a critical exponent $p = 1+2/N$ such
that blow-up of positive solutions always occurs for subcritical exponents,
whereas in the supercritical case global existence can occur for small
non-negative initial data.
