The present invention involves the use of a two-step membrane system for gas separations. In this two-step membrane system, the membrane system comprises high selectivity and high permeance membranes. The two-step membrane system includes a first membrane section, a second membrane section and an ejector configured to increase the pressure of a lower permeate using the energy from a higher permeate gas pressure. The process provides increase in product recovery and product purity of the product gases. It can also save the cost compared to the system using compressors and external energy to drive the separation of gases.