The description and analysis of non-stationary continuous control systems in the spectral range in non-orthogonal functions. Orthorecursive approach. Orthorecursive expansions are the generalization of the classical expansions of elements of the Hilbert space into Fourier series. In the article orthorecursive spectral characteristics for the description of signals and control systems are considered. The algorithms using orthorecursive spectral characteristics and intended for the description and analysis of linear non-stationary control systems with both deterministic and random input signals are designed. These algorithms are implemented in package MLSY - OSM - SH (the extension of Mathcad) which is destined for the analysis of integer and fractional order non-stationary continuous control systems by the spectral method in the system of the Faber-Schauder functions. The results are demonstrated with model examples of the elementary and typical operations of the spectral method.