In this thesis, we consider the identification of continuous-time multivariable systems. Direct methods of identification, i.e. identifying a continuous-time model directly from samples of input-output data, are considered briefly. Of primary consideration is the indirect method of identification, which can be considered as a two stage method. First, a discrete system model is identified from samples of input-output data. The next step is to transform this discrete time model to an equivalent continuous-time representation. The classical ZeroOrder hold (ZOH) transformation is presented primarily for comparison with the derived First-Order hold (FOH) technique. Involved in both of these methods is the transformation of the discrete-time state transition matrix to the continuous time system matrix. A new method for this transformation is presented also. This method along with the presented FOH transformation method have been published in Electronics Letters and another paper on this FOH method has been submitted as an invited paper at the 1991 IFAC Symposium on Identification.