Inthisarticle,weestablishtheglobalstabilityofanendemicequilibriumofmulti-groupSIRepidemicmodels,whichhavenotonlyanexchangeofinpidualsbetweenpatchesthroughmigrationbutalsocrosspatchinfectionbetweendifferentgroups.Asaresult,wepartiallygeneralizetherecentresultinthearticle[16].