In this paper, starting with the multistep methods and one-leg methods with variablecoefficients, we construct two classes of linearly implicit methods. For the linear autonomo-us system y'= Ay, these linearly implicit methods respectively are identical with certain im-plicit multistep and one-leg methods. Moreover, the first (2 k-p)terms of the local trunca-tion error in the linearly implicit and implicit one-leg methods are the same.