Abstract. A new family of one-step integration methods is presented herein. A free parameter is used to control the numerical properties and it can be considered as an indicator of numerical dissipation for the high-frequency modes. This family of methods can have unconditional stability, explicit formulation, and desired numerical damping, which implies that the low-frequency modes can be accurately integrated while the spurious growth of high-frequency modes can be suppressed or even eliminated. In addition, a zero damping ratio can be achieved. Since the unconditional stability and explicit formulation are integrated for the proposed method family, it can drastically reduce the computational e orts when compared with the traditional integration methods.