A lithium oxyhalide cell electrically connected in parallel with a lithium ion cell is described. Importantly, the open circuit voltage of the freshly built primary lithium oxyhalide cell is equal to or less that the open circuit voltage of the lithium ion cell in a fully charged state. This provides a power system that combines the high capacity of the primary cell with the high pulse power of the secondary cell. This hybrid power system exhibits increased rate capability, higher capacity and improved safety in addition to elimination of voltage delay in comparison to a comparable lithium oxyhalide cell discharge alone.