This paper investigates two classes of three-layer difference schemes with weights in the form αyt˚,n+βτ2 yt t,n+σ1Ayn−1+(E−σ1−σ2)Ayn+σ2Ayn+1 = ϕn andαyt˚,n+βτ2 yt t,n+A(σ1 yn−1+(E−σ1−σ2)yn+σ2 yn+1) = ϕn. It obtains some sufficient conditions for the stability in a defined norm and, also, in special cases we achieve conditions for stability which do not depend on the choice of norm