A process for the preparation of high purity propylene polymers carried out in the presence of a catalyst comprising the product obtained by contacting:(a) a solid catalyst component comprising Mg, Ti and at least a first internal electron donor compound (1ID) selected among the succinates and a second internal electron donor compound (2ID) selected among the 1,3-diethers, wherein the molar ratio of first internal donor over second internal donor 1ID:2ID is comprised between 4:6 and 9:1, with (b) an organo-aluminum compound, and optionally with (c) an external electron donor compound, said process being carried out at a temperature equal or higher than 78° C. and by employing a molar ratio of organo-aluminum compound over solid catalyst component (b):(a) of lower than 5.