Some simple instances of the motion of a material point in Friedmann-Lobachevsky space /1/ are constructed and investigated, on the assumption that the space, like Galilean space, is empty (i.e., contains no matter) and that the forces acting on the point, including the gravitational forces, constitute a factor extraneous to the space. Thus, the problem is being considered in the context of a rather unusual “relativistic” mechanics, distinct from relativisitc mechanics proper. As will be seen later, the difference is quantitatively small and can be regulated by slowly varying cosmological factors in the pseudo-Euclidean metric of the space of special relativity theory.