In this paper, new ideas from our previous paper (Rydzyska, 1989)-i.e., problems connected with the new equivalence principle-have been developed. It is conformed, that certain static particles from Bellert's space-time are equivalent to a free particle from classic Milne's space-time. Mention is made of the algebraic structure of Bellert's space-time from (Rydzyska, 1990b). The space-time interval in this space-time, and its connection with a probability and the physical meaning of this interval and probability, has been defined. In the last section we derive dynamical equations for Bellert's space-time, i.e., we do the foundations of Bellert's general relativity theory.