Random copolymers of propylene with ethylene, and optionally other olefins, comprising from 3.5% to 6.5% by weight of ethylene and having a melt flow rate (MFR) according to ISO 1133 (230° C., 2.16 Kg) of less than 10 g/10 min and a melting temperature (Tm), determined by DSC, satisfying the relation: 45° C.≦Tm+C≦150° C. wherein C is the quantity (by weight) of ethylene in the copolymer. The random copolymers of the invention are specifically suited for cast film and/or sheet applications.