Some comparative theorems are given for the oscillation and asymptotic behavior for a class of high order delay parabolic differential equations of the form {A formula is presented} where n is an odd integer, Ω is a bounded domain in Rm with a smooth boundary ∂Ω , and Δ is the Laplacian operation with three boundary value conditions. Our results extend some of those of [P. Wang, Oscillatory criteria of nonlinear hyperbolic equations with continuous deviating arguments, Appl. Math. Comput. 106 (1999), 163-169...