Oil-injected multistage compressor device including a low-pressure compressor element (2) with a gas inlet (4a) for gas to be compressed and a gas outlet (5a) for low-pressure compressed gas and a high-pressure stage compressor element (3) with a gas inlet (4b) for low-pressure compressed gas and a gas outlet (5b) for high-pressure compressed gas. The gas outlet (5a) of element (2) is connected to inlet (4b) of element (3) via a conduit (6). The conduit (6) has a regulatable intercooler (9) configured to regulate the temperature at the gas inlet (4b) of the high-pressure stage compressor element (3) so that it is above the dew point. The intercooler (9) includes a regulatable air cooler and/or a regulatable water cooler, and is configured to adjust the temperature of the air or water by using a bypass conduit (16) and/or by screening off part of the intercooler (9).