Let \(X\) and \(Y\) be normed linear spaces and \(T\) be a linear relation from \(X\) into \(Y\), i.e., a set-valued map \(T\: X\to 2^Y\) (\(Tx=\emptyset \) being also allowed). Its conjugate \(T'\) from \(Y'\) into \(X'\) is defined by \(x'\in T'y'\iff y'y-x'x=0\) \(\forall x\in X\) \(\forall y\in Tx\). The author gives necessary and sufficient conditions ensuring that \((ST)'= T'S'\). This extends the analogous results of \textit{K.-H.\,Förster} and \textit{E.-O.\,Liebetrau} [Stud.\ Math.\ 59, 301--306 (1977; Zbl 0348.47021)] for operators. Various useful properties of linear relations are established along the way.