Multiprocessor systems are more susceptible to failure than conventional uniprocessor machines. Thus the design of schemes that enhance the fault tolerance capabilities of the algorithmic aspects of several problems that arise in conjunction with the design of such schemes will be done. The main thrust of this investigation is on some recently proposed on-line techniques that accomplish fault detection concurrently with normal computation. The main goals of this research are to develop practical and efficient schemes for fault detection and location and to obtain a better understanding of the issues involved in the design of fault tolerance schemes for multiprocessor systems.