A multi-cyclone separator of a multi-stage fluid filter for cleaning gaseous fluid is provided with a plurality of cyclone cells for separating particles and/or liquid from the gaseous fluid. The cyclone cells each have an inlet for the gaseous fluid to be purified, an outlet for the gaseous fluid freed of particles and liquid, and at least one discharge window discharging the separated particles and liquid. At least one discharge chamber is provided, and the discharge windows of the cyclone cells open into the at least one discharge chamber. At least one discharge opening leads out of the at least one discharge chamber. The at least one discharge chamber tapers in a funnel shape toward the at least one discharge opening. A multi-stage fluid filter is provided with the multi-cyclone separator that is arranged upstream of a main filter of the multi-stage fluid filter.