Single-stage vapour compression refrigeration system was compared with an actual vapour compression cycle, single-stage process with internal heat exchanger, and a two-stage process with economiser using the refrigerants of HCFC-22, CFC-502 and their alternatives such as HFC-134a, HFC-32, HFC-152a, HFC-404A, HFC-407C, HFC-507, HFC-410A. A theoretical performance study on a cascade refrigeration system was performed using two refrigeration cycles connected through the heat exchanger in the middle working as the evaporator for the high pressurized cycle and condenser for the low pressurized cycle. Other performance study was performed using a two-stage cascade refrigeration system having low and high pressure compressors connected through the mixing chamber in the middle. The condensation temperatures were between 30 and 50 °C, evaporation temperatures were between −50 °C and 5 °C and heat exchanger and economiser temperatures were kept as constant for the comparisons. Some of the alternative refrigerants’ coefficients of performance values are found to be higher than their base traditional pure refrigerants. The effects of the main parameters of performance analysis such as refrigerant type, degree of subcooling, and superheating on the performance coefficient, refrigerant charge rate and volumetric refrigeration capacity are investigated for various operating conditions as case studies.