A compression device includes a first compressor and a second compressor mounted in parallel, each compressor including a leakproof enclosure including a low pressure portion containing a motor and an oil sump, an oil level equalization conduit putting into communication the oil sumps of the first and second compressors, and control means adapted for controlling the starting and the stopping of the first and second compressors. The first compressor includes first detection means coupled with the control means and adapted for detecting an oil level in the oil sump of the first compressor. The control means are adapted for controlling the stopping of the second compressor when the oil level detected by the first detection means falls below a first predetermined value.