Screening for alternative refrigerants with high energy efficiency and low environmental impacts is one of the highest challenges of the refrigeration sector. This paper investigates the performance and refrigerant screening for single and two stages vapor compression refrigeration cycles. Several pure hydrocarbons, hydrofluorocarbons, hydrofluoroolefins, fluorinated ethers, and binary azeotropic mixtures are proposed as alternative refrigerants to substitute R22 and R134a due to their environmental impacts. The BACKONE equation of state is used to compute the thermodynamic properties of the candidates. The results show that the maximum coefficients of performance (COP) for single and two stage cycles using pure substances are achieved using cyclopentane with values of 4.14 and 4.35, respectively. On the other side, the maximum COP for the two cycles using azeotropic mixtures is accomplished using R134a + RE170 with values of 3.96 and 4.27, respectively. The two-stage cycle presents gain in COP between 5.1% and 19.6% compared with the single-stage cycle based on the used refrigerant. From the obtained results, among all investigated refrigerants, cyclopentane is the most suitable refrigerant for the two cycles from the viewpoint of energy efficiency. However, extra cautions should be taken due to its flammability.