This paper presents the results of analysis of energy and economic efficiency of the hierarchical gas-gas engine, with a note that a trigeneration system was analyzed, in which the production of electricity, heat and cold are combined. This solution significantly increases the energy efficiency of the gas and gas system compared to a system without cold production. The analysis includes a system comprising a compressor chiller which is driven by an electric motor in the system, as well as a system applying the mechanical work that is carried out via a rotating shaft of rotor-based machines, i.e., a gas turbine and a turboexpander. The comfort of the regulation of the refrigerating power rather promotes the use of a solution including an electric motor. Analysis contains also a schematic diagram of the system with a absorption chiller, which is driven by low-temperature enthalpy of exhaust gases extracted from a hierarchical gas-gas engine. Application of turboexpander with heat regeneration in the trigeneration system is also analyzed. Based on the multi-variant economic and thermodynamic calculations, the most favorable system variant was determined using, among others, the specific cost of cold production.