The method for making a multilayer composite having one or more colors brings together a number of acrylic layers, which are partially cured in a first step and completely cured in a second step. The curing takes place with actinic radiation, such as accelerated electrons, UV radiation or X-ray radiation, the curing unit operating with different dosage rates during the two steps. The curable acrylic layers are applied to the respective supporting layers by screen printing or stencil printing, or else may be applied to the supporting layers by casting or with the aid of printing rollers.