An accurate and highly efficient algorithm series for structural stationary/non-stationary random response analysis, pseudo excitation method (PEM) is presented. The algorithm series, which have been developed since early 1980s, applies to the randow vibration analyses of structuses subjected to single/multiple, stationary/non-stationary random excitations, including the very attractive issuethe solution of the response to non-uniformly modulated evolutionary random excitations. Each algorithm in this series is an accurate complete quadratic combination (CQC) method because the cross-correlation quadratic terms between the participant modes and between the excitations have both been included. Such algorithms are easy to use because structural stationary random response analysis is reuced to the analysis of structural harmonic response, while structural non-stationary random responses can be readily computed in terrms of any step-by-step integration scheme (e. g. Newmark scheme or the precise integration method).