The piston motion of HFPE (hydraulic free-piston engine) was determined by the forces acting on the mover rather than on the crankshaft. This makes the complex interaction coupling between the piston motions and the combustion process. These factors lead to the combustion in the HFPE unstable rather easily. In this study, cycle-to-cycle variations in an HFPE combustion process and their correlations were investigated. Fifty consecutive cycles under steady-state operations were selected from the experimental data for this study. To evaluate the cyclic variation in the HFPE combustion process, the CoV(coefficient of variation) and the parameter correlations were redefined because the working principles of an HFPE differ from those of a conventional engine. Therefore, cyclic variations in the combustion parameters were investigated, and the CoV and correlation coefficients were calculated. Strong correlations were observed both between the piston velocity and the ignition delay period of combustion, and between the IMEP (indicated mean effective pressure) and the rapid combustion phase. The results show that the cyclic variations in an HFPE are primarily due to the "free" piston. These results provide theoretical basis for controlling the cyclic variations in an HFPE. (C) 2014 Elsevier Ltd. All rights reserved.