This thesis investigates the ability of a hovering bicopter to be self-stabilized in pitch and roll without the use of electronic sensors in those directions. A mathematical model of aircraft dynamics is developed in which the non-cyclic proprotors are allowed to precess freely as gyroscopes since these are known to embody stabilizing elements. In the prior art of bicopter oblique active tilting (OAT), the proprotors generate gyroscopic control moments only when forcibly tilted, and stabilization in pitch and roll requires electronic attitude sensors and actuator servos. A self-stabilized system, however, would reduce cost, stresses and energy consumption, and could be scalable without limit. Through analysis of the characteristic equations it is found that aircraft angular positions cannot be so stabilized, but their velocities can be, maintaining the benefits listed above. This stability is similar to that due the flybar damping system of early Bell helicopters and still useful in small models today.