In this paper, we study blow-up phenomena of the following p-Laplace type nonlinear parabolic equations under nonlinear mixed boundary conditions and u = 0 on Γ₂ × (0, t*) such that Γ₁ ∪ Γ₂ = ∂Ω, where f and h are real-valued C¹-functions. To discuss blow-up solutions, we introduce new conditions: For each x ∈ Ω, z ∈ ∂Ω, t > 0, u > 0, and v > 0, for some constants α, β₁, β₂, γ₁, γ₂, and δ satisfying where ρm := infw > 0ρ(w), P(v)=∫₀vρ(w)dw, F(x, t, u)=∫₀uf(x, t, w)dw, and H(x, t, u)=∫₀uh(x, t, w)dw. Here, λR is the first Robin eigenvalue and λS is the first Steklov eigenvalue for the p-Laplace operator, respectively.