The paper mainly deals with the problem of reference of proper names. Unlike definite descriptions, proper names in themselves possess no exact necessary and sufficient conditions for making successful performance of reference. This is the consequence of the fact that proper names just name their bearers and do not describe them. It is argued that Frege’s theory violates this fact, and therefore can be taken only as a view about the meaning of proper names, not as a theory of reference. Two conceptions of Strawson designed to solve the problem are mentioned – the cluster description theory and the communication chain theory. The second one is refused immediately, as unrealistic view on referential behaviour of proper names. Then Searle’s version of cluster description theory, more elaborate one than Strawson’s, is analyzed. However, it is shown that this conception is unsatisfactory as well, because either it invokes Kripke’s and Donnellan’s objections against any description theory or its explanation of reference of proper names is circular.