Software reliability prediction is as vital to the software industry as to any other industry that relies on the quality of software. Reliability prediction, however, requires a solid model of the behaviour of the software system and a well suited prediction methodology and algorithms. The paper focuses on the second task. Optimal estimation techniques are applied to predict the future behaviour of software systems. An initial implementation of the proposed methodology has shown encouraging results. The observed discrepancy between the real and estimated values of the mean time to failure of software systems was low and sometimes around zero.