The zero error capacity of 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 of are studied; upper and lower bounds and methods of evaluation of are given. Inequalities are obtained for the relating to the "sum" and "product" of two given channels. The analogous problem of zero error capacity for 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 evaluating .