The Parallel Combustion Two-Stroke is an internal combustion engine utilizing a hypocycloid gear mechanism and parallel combustion chambers. The hypocycloid mechanism provides mechanical balance and linear rod motion which eliminates piston sidewall forces and creates two chambers in the working cylinder. These two chambers are connected to combustion chambers external to the working cylinder. The resulting engine operates on a two-stroke cycle with many of the advantages of a four-stroke engine. It operates as an internal combustion engine with many of the advantages of an external combustion engine. And it operates as a reciprocating engine with the dynamic balance of a rotary engine.