We study the nonlocal parabolic equation ut - Δu = ∫ 0t k(t; s) |u|p-1u(s) ds with p > 1. We assume that k is continuous and there exists γ∈ℝ such that k(Λt; Λs) = Λ-γk(t; s) for all Λ > 0, 0 < s < t. We consider the problem in ℝN and a Dirichlet problem in a bounded smooth domain Ω We analyze the conditions for either blow up or global existence of solutions.