The paper introduces a new family of unconditionally stable one-step methods for the direct integration of structural dynamics equations, which exhibit improved algorithmic damping properties that can be continuously controlled. The methods are compared with the Newmark family, Houbolt, and Wilson methods. The new algorithms are designed to be unconditionally stable, possess numerical dissipation controlled by parameters other than the time step, and not affect lower modes too strongly. The analysis includes a detailed examination of the amplification matrix and its eigenvalues to evaluate stability and accuracy. The results show that the new algorithms have better spectral radii and damping ratios compared to the Wilson and Houbolt methods, indicating improved performance in both higher and lower modes. The new family of algorithms is shown to be more accurate in the lower modes while being more strongly dissipative in the higher modes, making it a superior choice for structural dynamics simulations.The paper introduces a new family of unconditionally stable one-step methods for the direct integration of structural dynamics equations, which exhibit improved algorithmic damping properties that can be continuously controlled. The methods are compared with the Newmark family, Houbolt, and Wilson methods. The new algorithms are designed to be unconditionally stable, possess numerical dissipation controlled by parameters other than the time step, and not affect lower modes too strongly. The analysis includes a detailed examination of the amplification matrix and its eigenvalues to evaluate stability and accuracy. The results show that the new algorithms have better spectral radii and damping ratios compared to the Wilson and Houbolt methods, indicating improved performance in both higher and lower modes. The new family of algorithms is shown to be more accurate in the lower modes while being more strongly dissipative in the higher modes, making it a superior choice for structural dynamics simulations.