This paper is concerned with the computation of pseudovariety joins involving the pseudovariety LI of locally trivial semigroups. We compute, in particular, the join of LI with any subpseudovariety of CRmN, the Mal'cev product of the pseudovariety of completely regular semigroups and the pseudovariety of nilpotent semigroups. Similar studies are conducted for the pseudovarieties K, D and N, where K (resp. D) is the pseudovariety of all semigroups S such that eS = e (resp. Se = e ) for each idempotent e of S.INVOTAN, grant 4/A/94/P
