In this note we consider the third order linear difference equations of neutral type (E) ∆ 3 [x(n) − p(n)x(σ(n))] + δq(n)x(τ (n)) = 0, n ∈ N(n0), where δ = ±1, p, q : N(n0) → ℝ+; σ, τ : N(n0) → ℕ, lim n→∞ σ(n) = lim n→∞ τ (n) = ∞. We examine the following two cases: {0 < p(n) ≤ 1, σ(n) = n + k, τ (n) = n + l}, {p(n) > 1, σ(n) = n − k, τ (n) = n − l}, where k, l are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.