  In this work 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 of the methods.
