A class of two-beam interferometers, insensitive to mirror tilt, is discussed. The mirrors at the ends of each arm of the interferometer are parallel and rigidly connected and these are moved to change the optical path. If the beams in the two arms have a relative twist of 180°, tilt of this pair of mirrors does not change the interference pattern. Polarization effects in such interferometers can be serious; their compensation is discussed.