An engine has a pair of rotors, both housed within the same housing. The housing has an interior cavity which is preferably spherical but need only be partially spherical, the remainder at least having rotational symmetry. Each rotor is mounted on an axis that passes through the center of the cavity, the respective axes of the rotors being at an angle to each other, with the center of each rotor being at the center of the cavity. The rotors interlock with each other to define chambers. Vanes or pistons defined by a contact face and a side face protrude from the rotors. The side faces and contact faces, and the housing interior define chambers that open and close as the rotors rotate. Each contact face of one rotor is defined by the rotation of a conical section of material on the other rotor, so that there is constant linear contact between opposing vanes on the two rotors, at least on one side of the engine. The rotors may face each other or be one inside the other. When one is inside the other, the engine may be used in association with an external combustor. Bearings support the rotors for rotation, and ports are used to allow gases into and out of the chambers.