SwissFEL is a Free Electron Laser (FEL) facility being constructed at PSI, based on a 5.8GeV normally conducting main linac. A photocathode gun will generate two bunches with 28ns spacing at 100Hz repetition rate, with a nominal charge range of 10-200pC. A fast beam distribution kicker will allow to distribute one bunch to a soft X-ray undulator line and the other bunch to a 0.1nm hard X-ray undulator line. The SwissFEL electron beam position monitor (BPM) system will employ three different types of dual-resonator cavity BPMs, since the accelerator has three different beam pipe apertures. In the injector and main linac (38mm and 16mm aperture), 3.3GHz cavity BPMs will be used, where a low Q_L of ~40 was chosen to minimize crosstalk of the two bunches. In the undulators that just have single bunches and 8mm BPM aperture, a higher Q_L will be chosen. This paper reports on the development status of the SwissFEL BPM system. Synergies as well as differences to the E-XFEL BPM system will also be highlighted.