In　this　paper,　the　hypothesis　testing　and　interval　estimation　for　the　intraclass　correlation　coefficients　are　considered　in　a　two-way　random　effects　model　with　interaction.　Two　particular　intraclass　correlation　coefficients　are　described　in　a　reliability　study.　The　tests　and　confidence　intervals　for　the　intraclass　correlation　coefficients　are　developed　when　the　data　are　unbalanced.　One　approach　is　based　on　the　generalized　pi-value　and　generalized　confidence　interval,　the　other　is　based　on　the　modified　large-sample　idea.　These　two　approaches　simplify　to　the　ones　in　Gilder　et　al.　[2007.　Confidence　intervals　on　intraclass　correlation　coefficients　in　a　balanced　two-factor　random　design.　J.　Statist.　Plann.　Inference　137,　1199-1212]　when　the　data　are　balanced.　Furthermore,　some　statistical　properties　of　the　generalized　confidence　intervals　are　investigated.　Finally,　some　simulation　results　to　compare　the　performance　of　the　modified　large-sample　approach　with　that　of　the　generalized　approach　are　reported.　The　simulation　results　indicate　that　the　modified　large-sample　approach　performs　better　than　the　generalized　approach　in　the　coverage　probability　and　expected　length　of　the　confidence　interval.　(C)　2008　Elsevier　B.V.　All　rights　reserved.