Summary: Let \(A\) be a representation-finite algebra. We show that a finite dimensional \(A\)-module \(M\) degenerates to another \(A\)-module \(N\) if and only if the inequalities \[ \dim_K\operatorname{Hom}_A(M,X)\leq\dim_K\operatorname{Hom}_A(N,X) \] hold for all \(A\)-modules \(X\). We prove also that if \(\text{Ext}_A^1(X,X)=0\) for any indecomposable \(A\)-module \(X\), then any degeneration of \(A\)-modules is given by a chain of short exact sequences.