Time is one of the most fundamental ideas in hard sciences generally and in Physics particularly. Physicists know two essentially different conceptions of time, the relational one and the substantial one (the latter is based on Kozyrev’s “Causal Mechanics”). According to the former there exists no time “per se” in nature, and time is no more than a relation between physical events. That is, time is a specific manifestation of the properties of physical bodies and changes occurring in them. The latter, the substantial one, assumes, vice versa, that time is an independent phenomenon of nature, a specific kind of substance, coexisting with space, matter and physical fields. The relational conception of time is associated with the names of Aristotle, Leibnitz and Einstein. The most ardent adherents of the substantial conception of time are Democritus, Newton and Kozyrev. Modern Physics is built on the basis of the relational conception of time. However, the use of this conception has not so far resulted in resolving all the problems related to time. Moreover, so far even an essential definition of time has not been formulated in Physics, there are only operational definitions indicating different methods of measuring time intervals. The adherents of the substantial conception of time, including N.A.Kozyrev, for their part, have not answered all the questions concerning time and have not given a rigorous mathematical formalism describing the time substance. Hence one can state that nowadays both the relational and substantial conceptions of time are certain points of view rather than physical hypotheses developed in detail. Each of them has its own positive aspects. The positive feature of the substantial conception lies in that it gives the researcher carte blanche for creative search, which may promote a successful resolution of the problem of the time phenomenon.