Consider the first order linear difference equation with general advanced argument and variable coefficients of the form $$\nabla x\left(n\right)-p\left(n\right)x\left(\tau \right(n\left)\right)=0,n⩾1,$$ where p(n) is a sequence of nonnegative real numbers, τ(n) is a sequence of positive integers such that $$\tau \left(n\right)⩾n+1,n⩾1,$$ and ▿ denotes the backward difference operator ▿x(n) = x(n) − x(n − 1). Sufficient conditions which guarantee that all solutions oscillate are established. Examples illustrating the results are given.

In this paper, sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form $$y_{n+3}+r_n{y}_{n+2}+q_n{y}_{n+1}+p_n{y}_n=0,n\ge 0.$$ These results are generalization of the results concerning difference equations with constant coefficients $$y_{n+3}+r{y}_{n+2}+q{y}_{n+1}+p{y}_n=0,n\ge 0.$$ Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with help of a class of linear second order difference equations.