The zero error capacityC_oof a noisy channel is defined as the least upper bound of rates at which it is possible to transmit information with zero probability of error. Various properties ofC_oare studied; upper and lower bounds and methods of evaluation ofC_oare given. Inequalities are obtained for theC_orelating to the "sum" and "product" of two given channels. The analogous problem of zero error capacityC_oFfor a channel with a feedback link is considered. It is shown that while the ordinary capacity of a memoryless channel with feedback is equal to that of the same channel without feedback, the zero error capacity may be greater. A solution is given to the problem of evaluatingC_oF.