This invention relates to high impact strength polymer blends containing at least two two-phase or multiphase polymers P1 and P2, which in turn contain at least one toughening phase A1 or A2 and at least one hardness phase B1 or B2. B1 and B2 differ in chemical structure and are thermodynamically compatible with one another. The polymer blend optionally contains another thermoplastic polymer B'3 and/or another two-phase or multiphase polymer P4 contain at least one toughening phase A4 and at least one hardness phase B4, provided that B'3 and/or B4 are different from B1 and B2 and are thermodynamically compatible with B1 and B2.