A method of using a shelf-stable two-part self-adhering dental composition that comprises (a) at least one acidic compound containing at least one acidic moiety selected from the group consisting of ##STR00001## where R is an alkyl or aryl group; (b) at least one polymerizable monomer without any acidic group where the polymerizable group is selected from the group consisting of an acrylate, a methacrylate and a vinyl group; (c) a substituted thiourea selected from the group consisting of 1-(2-pyridyl)-2-thiourea and 1-(2-tetrahydrofurfuryl)-2-thiourea; and (d) a hydroperoxide compound with at least one hydroperoxide group attached to a tertiary carbon. The first and second parts are then mixed immediately prior to application, applied to a dental substrate, and hardened. The bond strength of the mixed composition to dentine substrate is at least 3 MPa. The composition has excellent shelf-life and is self-adhering to various dental substrates such as a tooth, metal alloy and porcelain. It can be used as a filling material, a cement, a liner/base, a pit/fissure sealant, a primer or an adhesive.