Abstract: We invesigated the oscillation of the solution of the secondorder mixed partial difference equation with two constant coefficients pU_m+2,n+qU_m,n+2-U_m,n+U_m+σ,n-τ=0 by using the envelope theory, and obtained three necessary and sufficient conditions for the oscillation of solutions of the equation,  where σ and τ are positive integers, m and n are nonnegative integers, p and q are real numbers.

Key words: oscillation, characteristic equation, mixed partial difference equation