The present invention relates to a process for the enzymatic production of a dipeptide composition from a cyanophycin (CGP) or CGP-like polymer preparation by degrading the polymer preparation with an CGPase, a CGPase particularly adapted for said process, and the use of cyanophycin (CGP) or CGP-like polymers or fragments thereof, notably a dipeptide composition obtained by the process as defined above, as pharmacetical composition, medicament, or as food or feed substitute.