The claimed invention relates to the downhole systems for extracting various fluids, in particular—for simultaneous extraction out of a number of producing formations. The inventive downhole system comprises a casing pipe and a tubing extending through said casing pipe, between which pipe and tubing formed are separate isolated cavities. Each one of which cavities communicates, via perforations, with a respective producing formation. In each one of the isolated cavities, to the tubing coupled is a hydraulic machine comprised by a motor and pump. The hydraulic machines in different isolated cavities being adapted to be adjusted independently. This system permits simultaneous extraction of fluids out of different producing formations, with independent controlling of such extraction in various formations. The claimed invention also relates to an immersion hydraulic machine used for extracting fluids.