A two-stroke opposite rotary-piston engine comprises a cylinder block including a sleeve and two pistons slidely disposed therein, oppositely movable forming a common combustion chamber and a first gap with sleeve's sidewalls, a rotor having a surface formed by an ellipse or Cassini line, traverses attached to the pistons, rollers attached to the traverses and springly depressed against the rotor, oil tubes with end bushings, oil supply and withdraw means, two plungers disposed in each tube forming a second gap essentially less than the first. The plungers are attached to the traverses and oppositely movable, including through channels, outward surfaces with the bushings forming external spaces, and inward surfaces with the tube sidewalls forming an internal space communicating with the oil supply and withdraw means. Oil drain means communicate the external spaces with the oil supply means. The engine absorbs side and inertial forces, is more efficient and clean.