Novel membrane compositions are prepared from polymers comprising tertiary amine containing polyamideamine functional groups. The membranes are durable, highly selective and have excellent homogeneity and high diffusivity. Asymmetric membranes can be prepared by solution casting or melt processing techniques can be used to produce homogeneous, high performance, symmetric membranes. The specific compositions of the membranes can be adjusted so as to achieve a membrane possessing a required degree of hydrophilicity and porosity. These membranes may be used in a variety of separation applications, particularly in two-phase solvent extraction.