Laser-engravable flexographic printing elements including a thermally crosslinked, elastomeric, laser-engravable relief-forming layer E are made by producing a multilayer composite which has at least a two-layer composite formed of a depot layer D and an uncrosslinked precursor layer V for the relief-forming layer E which is directly adjacent to the depot layer D. Optionally, the multilayer composite may include further layers, such as support foils or films and/or protective films. The precursor layer V most preferably includes at least one elastomeric binder, and at least one ethylenically unsaturated monomer and, optionally an absorber for laser radiation and/or further additives. The depot layer D most preferably includes at least one elastomeric binder, and at least one thermally decomposing polymerization initiator and, optionally, an absorber for laser radiation and/or further additives. The thermally decomposing polymerization initiators are allowed to diffuse out of the depot layer D into the precursor layer V. If desired the depot layer D may be removed. Thermal crosslinking of the precursor layer V thereby yields the crosslinked elastomeric, laser-engravable, relief-forming layer E.