\begin{document} The graph $H$ is $G$-good if the Ramsey number for the pair of graphs $G$ and $H$ is expressed as follows: $R(G,H)=(\chi (G)-1)(|V(H)|-1)+s(G),$ where $\chi(G)$ is the chromatic number of $G$ and $s(G)$ is the minimum cardinality of colour classes over all chromatic colourings of $V(G).$ We give the Ramsey number for a disjoint union of some $G$-good graphs versus a graph with components isomorphic to $G$ generalizing the results of Stahl [On the Ramsey number $r(F,K_m)$ where $F$ is a forest, Canad. J. Math. 27 (1975) pp.585--589], Baskoro et al. [Note. The Ramsey number for disjoint unions of trees, Discrete Math. 306 (2006) pp.3297--3301], Lin et al. [Ramsey goodness and generalized stars, Europ. J. Combin. 31 (2010) 1228--1234], and the previous results of the author [Ramsey numbers for a disjoint union of some graphs, Appl. Math. Lett. 22(2009) pp.475--477; Ramsey numbers for a disjoint union of good graphs, Discrete Math. 310(2010) pp.1501--1505]. \end{document}