A two-stroke opposite radial rotary-piston engine comprising: at least one module having a predetermined stroke length, said module including a stationary housing (130, 131); a stationary cylinder block assembled with the stationary housing (130, 131); two cylindrically shaped sleeves mounted on said block, each having inner sidewalls; an upper pair of pistons and a lower pair of pistons, wherein each said piston has a rod and a head situated oppositely to the rod, wherein one piston of the upper pair and one piston of the lower pair are slidely disposed within one of said sleeves, wherein the other piston of the upper pair and the other piston of the lower pair are slidely disposed within the other said sleeve, wherein the pistons positioned in each of said sleeves are oppositely linearly movable in relation to each other forming a common chamber defined by the pistons' heads, and wherein a portion of the inner sidewalls of the each of said sleeves is situated between the heads; characterized by a power takeoff shaft revolvably supported substantially by the stationary housing (130, 131); two substantially identical rotors fixedly mounted on the takeoff shaft outwardly in relation to the stationary housing (130, 131), wherein each of said rotors includes an inner operation surface,facing the stationary housing (130, 131), and is formed by a predeterminedly curved line of a closed type having a transverse axis and a longitudinal axis, wherein the corresponding axes of the two rotors are aligned in parallel, and wherein each of said rotors on the frontal part of its outer surface including a peripheral concaved surface portion made therein along said curved line; an upper cross-shaped traverse pair-wise spanning the rods of said upper pistons attached thereto, and a lower cross-shaped traverse pair-wise spanning the rods of said lower pistons attached thereto; two pairs of engagement units, wherein each of said two pairs of the engagement units is associated with one of said traverses, and wherein said engagement units operatively cooperate with said concaved surface portions of the rotors; two pairs of support bearings, wherein each of said two pairs of the support bearings is coupled to one of said traverses, and wherein each of said two pairs of the support bearings includes a bushing operatively rolling over the inner surface of the rotor, wherein said rolling impels the rotor; and guiding bearings essentially secured to the block and to the traverses, and mounted in the region of contact of said support bearings with said rotors. at least one module having a predetermined stroke length, said module including a stationary housing (130, 131); a stationary cylinder block assembled with the stationary housing (130, 131); two cylindrically shaped sleeves mounted on said block, each having inner sidewalls; an upper pair of pistons and a lower pair of pistons, wherein each said piston has a rod and a head situated oppositely to the rod, wherein one piston of the upper pair and one piston of the lower pair are slidely disposed within one of said sleeves, wherein the other piston of the upper pair and the other piston of the lower pair are slidely disposed within the other said sleeve, wherein the pistons positioned in each of said sleeves are oppositely linearly movable in relation to each other forming a common chamber defined by the pistons' heads, and wherein a portion of the inner sidewalls of the each of said sleeves is situated between the heads; characterized by a power takeoff shaft revolvably supported substantially by the stationary housing (130, 131); two substantially identical rotors fixedly mounted on the takeoff shaft outwardly in relation to the stationary housing (130, 131), wherein each of said rotors includes an inner operation surface,facing the stationary housing (130, 131), and is formed by a predeterminedly curved line of a closed type having a transverse axis and a longitudinal axis, wherein the corresponding axes of the two rotors are aligned in parallel, and wherein each of said rotors on the frontal part of its outer surface including a peripheral concaved surface portion made therein along said curved line; an upper cross-shaped traverse pair-wise spanning the rods of said upper pistons attached thereto, and a lower cross-shaped traverse pair-wise spanning the rods of said lower pistons attached thereto; two pairs of engagement units, wherein each of said two pairs of the engagement units is associated with one of said traverses, and wherein said engagement units operatively cooperate with said concaved surface portions of the rotors; two pairs of support bearings, wherein each of said two pairs of the support bearings is coupled to one of said traverses, and wherein each of said two pairs of the support bearings includes a bushing operatively rolling over the inner surface of the rotor, wherein said rolling impels the rotor; and guiding bearings essentially secured to the block and to the traverses, and mounted in the region of contact of said support bearings with said rotors.