The Taylor series is introduced to analyse and approximate the solution of a class of scaled systems. Using the operational matrix of integration, together with the derived scaled operational matrix, the dynamical equation of a scaled system is reduced to a set of simultaneous linear algebraic equations. The coefficient vectors of the Taylor series expansion can be determined recursively by the derived algorithm. The parameter identification problems of scaled systems are also investigated. Owing to the simplicity of the operational matrix of integration and the scaled operational matrix, the Taylor series presents considerable computational advantages when compared with the other possible polynomial series, provided that both the input and output signals are analytic functions oft.