The present invention discloses a conjugate comprising erythropoietin (EPO) and an asymmetric branched polymeric structure comprising two branches of monomethoxypolyethylene glycol (mPEG), where the molecular mass of one of these mPEG branches is between 10 kDa and 14 kDa, and the molecular mass of the other branch of mPEG is between 17 kDa and 23 kDa, as well as the pharmaceutical compositions containing it. The invention also provides a method for the preparation of pegylated EPO, wherein said protein is conjugated to an asymmetric branched polymeric structure with two branches of mPEG having the above described molecular masses.
