Consider the first initial-boundary value problem for parabolic equations such as L ϵu ≡ u t+ ϵ 4Δ 2u = ƒ(u) , L ϵu ≡ u t+ ϵ 4Δ 2u − Δu = ƒ(u) with f( u) superlinear, and denote the blow-up time of the solution by T ε . It is proved that T ε → T 0as ε → 0 where T 0 is the smallest blow-up time for L ou = ƒ(u). Since there is no maximum principle for higher order parabolic equations, one cannot use here traditional comparison methods. The main results are outlined in Section 1.