Abstract: This article deals with the conditions that ensure the blow-up
phenomenon or its absence for solutions of the system
u_t=△ u^l+u^p₁v^q₁ and v_t=△ v^m+u^p₂v^q₂ with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p₂q₁-(l-p₁)(m-q₂), the initial data, and the domain $\Omega$.

Key words: Global existence, blow-up, degenerate parabolic system