In the talk we present explicit Adams-type multistep methods with extended stability interval, which are analogous to the stabilized Chebyshev Runge–Kutta methods. It is proved that for any \(k\geq 1\) there exists an explicit \(k\)-step Adams-type method of order one with stability interval of length \(2k\). The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In general case to construct a \(k\)-step method of order \(p\) it is necessary to solve a constrained optimization problem in which the objective function and \(p\) constraints are second degree polynomials in \(k\) variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability properties of the methods.