The present application relates to a new catalyst system for the polymerization of olefins, comprising a new ionic activator having the formula: [R1R2R3AH]+ [Y]−, wherein [Y]− is a non-coordinating anion (NCA), A is nitrogen or phosphorus, R1 and R2 are hydrocarbyl groups or heteroatom-containing hydrocarbyl groups and together form a first, 3- to 10-membered non-aromatic ring with A, wherein any number of adjacent ring members may optionally be members of at least one second, aromatic or aliphatic ring or aliphatic and/or aromatic ring system of two or more rings, wherein said at least one second ring or ring system is fused to said first ring, and wherein any atom of the first and/or at least one second ring or ring system is a carbon atom or a heteroatom and may be substituted independently by one or more substituents selected from the group consisting of a hydrogen atom, halogen atom, C1 to C10 alkyl, C5 to C15 aryl, C6 to C25 arylalkyl, and C6 to C25 alkylaryl, and R3 is a hydrogen atom or C1 to C10 alkyl, or R3 is a C1 to C10 alkylene group that connects to said first ring and/or to said at least one second ring or ring system. The present application also relates to a process for the polymerization of olefins, preferably propylene, using this and other catalyst systems, as well as to polymers made by said process.