Abstract：We try to develop a unified approach to the uniform-in-time energy stability of a special class of linear two-step numerical methods when applied to some prototype linear dissipative problems. Also, some classical stability properties of these multi-step methods are analyzed.  We borrow the idea of Talor's expansion based on different time point $t^*$ in order to construct the generalized two-step methods, especially the generalized second-order Adams-Bashforth(AM2) method and the generalized second-order Backward differentiation formula(BDF) method. Naturally, we expect to make full advantage of these generalized two-step methods in some problems involving long-time behavior such as the coarsening process for the Cahn-Hilliard and several phase-field thin-film models. Lots of past research about the long-time stability issue of numerical schemes motivates us to explore whether the generalized AM2 method and the generalized BDF2 method can inherit the uniform-in-time energy bound in some linear dissipative problems. We eventually have some theoretical results about the uniform-in-time energy stability of the generalized AM2 and the generalized BDF2 methods in some prototype linear dissipative systems with a symmetric positive definite operator and a mild anti-symmetric operator. Additionally, some numerical results are given to show the advantages of these methods in accuracy and stability. On the other hand, we also try to explore the relationship between several stability properties, especially A-stability and uniform-in-time energy stability.