This study looks at motion of particles using mathematical methods of chronometric invariants (physical observable values in General Relativity). It is shown that aside for massbearing particles and light-like particles “zero-particles” can exist in fully degenerated spacetime (zero-space). For a regular observer zero-particles move instantly, thus transferring long-range action. Further we show existence of two separate areas in unhomogeneous spacetime, where observable time flows into future and into past, while this duality is not found in homogeneous space-time. These areas are referred to as our world, where time flows into future and as the mirror Universe, where time flows in past. The areas are separated with a space-time membrane, referred to as zero-space, where observable time stops. This is an electronic version of the book: Rabounski D.D. and Borissova L.B. Particles here and beyond the Mirror. Editorial URSS, Moscow, 2001.