Due to their high hemocompatibility and gas permeation capacity, bi-soft segment polyurethane/polycaprolactone (PU/PCL) polymers are promising materials for use in membrane blood oxygenators. In this work, both nonporous symmetric and integral asymmetric PU/PCL membranes were synthesized, and the permeation properties of the atmospheric gases N2, O2, and CO2 through these membranes were experimentally determined using a new custom-built gas permeation apparatus. Permeate pressure vs. time curves were obtained at 37.0 °C and gas feed pressures up to 5 bar. Fluxes, permeances, and permeability coefficients were determined from the steady-state part of the curves, and the diffusion and sorption coefficients were estimated from the analysis of the transient state using the time-lag method. Independent measurements of the sorption coefficients of the three gases were performed, under equilibrium conditions, in order to validate the new setup and procedure. This work shows that the gas sorption in the PU/PCL polymers is the dominant factor for the permeation properties of the atmospheric gases in these membranes.