The theory of fractional calculus goes back to the beginning of the theory of differential calculus but its inherent complexity postponed the application of the associated concepts. In the last decade the progress in the areas os chaos and fractals reveales subtle relationships with the fractional calculus leading to an aincreasing interest in the development of the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area os automatic control preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domain, which makes them suited for z-transform amalysis and discrte-time implementation. the performance of discrte-time fractional-order controllers with linear and nonlinear systems is also investigated.