This paper focuses on nonlinear dynamic analysis of a solar-powered free piston hot-air engine. First, dynamic and thermodynamic equations governing the free piston hot-air engine are extracted. Accordingly, by coupling the obtained relationships, nonlinear behavior of the free piston hot-air engine is simulated. Then, motion and velocity of the pistons in steady state condition are discussed using numerical solution of the nonlinear equations and using the phase plane analysis. Next, the stroke of pistons, maximum and minimum volumes and pressure as well as the produced work and power are studied corresponding to the change of temperatures in the hot and cold chambers. Since, the damping coefficient between power piston and the cylinder wall is variable due to the temperature changes and environmental conditions its effect on the stroke of pistons, maximum and minimum volumes, pressure, produced work and power is investigated. The results obtained clearly indicate that there is an optimal power for a certain value of damping coefficient. Then, stroke of the pistons, maximum and minimum volume and pressure as well as the produced work and power are studied according to the changes in engine parameters such as mass and stiffness of work and displacer pistons. The ranges of variations of engine parameters are selected so that the motions of displacer and power pistons fall into a limit cycle. Finally, sensitivity analysis of the produced power is carried out considering changes in engine parameters.