The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condi-tion when they are applied to neutral delay differential equations of the form y'(t) = ay(t) + by(t - τ) +cy'(t -τ) y(t) =g(t) -τ≤t≤0withτ＞0anda, bandc ∈ C , and it is proved that the ‖Bn ‖ is suit-ably bounded, where B is the companion matrix.