An improved elliptical path exercise machine is provided that is simple and robust in its construction, requires minimal maintenance, provides smooth even exercise motion, and which has a compact foot-print. The apparatus includes a pair of planetary gears, sun/ring gears and at least one crank. The crank is supported and arranged so as to be rotatable about a crank axis. Each planetary gear is pivotably secured to the crank about a pivot point located and arranged such that as the crank is rotated the planetary gears engage and rotate relative to their corresponding sun/ring gears while simultaneously revolving about the crank axis so as to form right and left epicylic gear trains. Two foot pedals are each pivotably secured to a corresponding one of the planetary gears and are sized and arranged to support the feet of a user. The layout and geometries of the device are such that each foot-pedal follows a substantially elliptical foot-path as the crank is rotated. The major axis of the elliptical foot-path is greater than twice the effective crank-arm length of the crank so that a compact foot print is attained.