A method for removing a radiation-polymerized cosmetic coating from nails comprising applying a solvent system comprising a hydroxyl-containing solvent and a non-hydroxyl-containing solvent to a polymerized nail coating. A two package system comprising a first package comprising polymerizable nail coating composition comprising a (meth)acrylic oligomer, (meth)acrylic monomer, or a mixture of a (meth)acrylic oligomer and a (meth)acrylic monomer, and a photoinitiator, wherein the oligomer or monomer has an acidic or basic ionizable group and a second package comprising a solvent system for removing the polymerizable nail coating composition after it has been applied to a nail and radiation cured, the solvent system comprising a hydroxyl-containing solvent and a non-hydroxyl-containing solvent. A radiation-curable coating composition for human nails is also disclosed.