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In the paper a comparison is made between two approximate methods of system analysis based on the use of the operational matrices of integration and differentiation. Both methods applied to model problems involving linear time-invariant differential equations yielded results of equal order of accuracy for the same number of orthogonal polynomial terms. However, the operational matrix of differentiation method is not limited to initial-value problems, but may easily be applied to boundary-value problems. In addition, due to the exact definition of this matrix, transformations from an orthogonal polynomial base to another may easily be performed with the use of the operational matrix of polynomial series transformation. The operational matrix of differentiation approach may be easily applied to the analysis of other types of systems such as time-varying and distributed parameter systems, and can be easily extended …