Compositionistheoperationofreplacingvariablesinapolynomialwithotherpolynomials.Themainquestioninthispaperis:whendoescompositioncommutewithuniversalGroebnerbasiscomputation?Weprovethatthishappensiffthecompositionissinglevariable.ThishasanaturalapplicationinthecomputationofuniversalGroebnerbasesofcomposedpolynomials.