A method is described for the site-specific preparation of hGRF-PEG conjugates containing one or more PEG units (per mole of hGRF) covalently bound to Lys.sup.12 and/or Lys.sup.21 and/or N.sub..alpha., characterized in that the conjugation reaction between the hGRF peptide and activated PEG is carried out in solution and the desired hGRF-PEG conjugate can be purified by chromatography. The conjugates prepared by this method, as well as their use in the treatment, prevention of diagnosis of growth hormone deficiency, are also an object of the present invention.