The invention relates to a GLP-1 prodrug of the general formula I: R1-(NHXaa1)- Xaa2-(OHis)-(GLP-1peptide) (Formula I), wherein GLP-1 peptide is GLP-1(8-37) (SEQ ID NO: 1) or an analogue thereof having a maximum of nineamino acid changes as compared to GLP-1(8-37), R1 is lower alkyl, (NHXaa1) is an amino acid, Xaa2 is an amino acid, and (OHis) is a radical of imidazole-lactic acid or a pharmaceutically acceptable salt, amide, or ester of the prodrug. The invention also relates to specific GLP-1 parent drugs of the general formula II: (HOHis)-(GLP-1peptide) (Formula II), as well as specific intermediate products. The invention furthermore relates to a method of achieving release in vivo of an active and stabilised GLP-1 parent drug of the general formula II: (HOHis)-(GLP-1 peptide), by administering a GLP-1 prodrug as well as to such GLP-1 prodrug, and such GLP-1 parent drug, respectively, for use as a medicament, in particular for use in the treatment and/or prevention of all forms of diabetes and related diseases. The prodrug may be used to alter the PK and/or absorption profile of the drug, for example to a desirable bell-shaped curve. The parent drug has a good biological activity, and is stabilised against degradation by DPP- IV.Linvention concerne un promédicament à base de GLP-1 de formule générale I : R1-(NHXaa1)-Xaa2-(OHis)-(peptide de GLP-1) (formule I), dans laquelle peptide de GLP-1 représente GLP-1 (8-37) (SEQ ID NO : 1) ou un analogue de celui-ci présentant un maximum de neuf changements dacides aminés comparativement à GLP-1 (8-37), R1 représente un alkyle inférieur, (NHXaa1) représente un acide aminé, Xaa2 représente un acide aminé et (OHis) représente un radical dacide imidazole-lactique ou un sel, un amide ou un ester pharmaceutiquement acceptable du promédicament. Linvention concerne également des médicaments parents à base de GLP-1 de formule générale II : (HOHis)-(peptide de GLP-1) (formule II), ainsi que des produits intermédiaires spécifiques.