A process for producing terpolymers of propylene, comprising a) feeding into a slurry reactor a reaction mixture containing 50-85 w-% of propylene, 1-10 w-% of ethylene, 15-40 w-% of another C4-C8 alpha-olefin, a catalyst system maintaining olefin polymerization at said temperature conditions, and optionally hydrogen, b) polymerizing said reaction mixture at a temperature of lower than 70° C. a sufficient time to obtain a propylene terpolymer amounting to 50-99 w-% of the end product, c) transferring said reaction mixture into a gas phase reactor operating at a pressure of higher than 5 bars, preferably higher than 10 bars, optionally adding 0-30 w-% of ethylene, 0-10 w-% of another C4-C8 alpha-olefin, 0-40 w-% of propylene and optionally hydrogen, and d) continuing polymerization in said gas phase reactor for obtaining a propylene terpolymer amounting to 1-50 wt-% of the end product. The terpolymer has a melting temperature a less than 135° C., preferably less than 132° C., and it can be used for manufacturing films having good sealing properties.