This paper discusses the effects of variations in system parameters on the dynamic behavior of a Free-Piston Stirling Engine/Linear Alternator (FPSE/LA)-load system. The mathematical formulations incorporate both the mechanical and thermodynamic properties of the FPSE, as well as the electrical equations of the connected load. State-space technique in the frequency domain is applied to the resulting system of equations to facilitate the evaluation of parametric impacts on the system dynamic stability. Also included is a discussion on the system transient stability as affected by sudden changes in some key operating conditions.Some representative results are correlated with experimental data to verify the model and analytic formulation accuracies. Guidelines are given for ranges of the system parameters which will ensure an overall stable operation.