The problem of the sensitivity analysis of systems involving λ-variations may be treated by a new method based on the idea of solving the sensitivity equation of a system using orthogonal functions. Though the presented method is based on the set of block-pulse functions it can also be used for other sets of orthogonal functions. The approach can also be applied for solving other problems of a similar nature (inversion of Laplace transform involving Dirac impulses, analysis of singular perturbed systems etc.).