This paper is on production planning and inventory control in systems where manufacturing and remanufacturing operations occur simultaneously. Typical for these hybridsystems is, that both the output of the manufacturing process and the output of the remanufacturing process can be used to fulfill customer demands. Here, we consider a relatively simple hybrid system, related to a single component durable product. For this system, we present a methodology to analyse a PUSH control strategy (in which all returned products are remanufactured as early as possible) and a PULL control strategy (in which all returned products are remanufactured as late as is convenient). The main contributions of this paper are (i) to compare traditional systems without remanufacturing to PUSH and to PULL controlled systems with remanufacturing, and (ii) to derive managerial insights into the inventory related effects of remanufacturing.