A bleeding or fugitive printing ink is disclosed and claimed which can be printed by the method of dry or wet offset or letterpress. This ink allows, when printed on security documents and dried, to prevent attempts of forgery or counterfeit in that the ink contains at least one dyestuff which is sensitive to organic solvents and other chemical reagents. The ink, when printed, forms a solid, polymerised or cross-linked binder matrix on the surface of the document when the printings are submitted to energy radiation, or by an oxypolymerisation reaction. This matrix is formed nearly immediately, in the case of oxypolymerisation within 24 hours, in contrast to conventional bleeding printing inks whose matrixes do not really dry and remain liquid in the interstices of the substrate.