Abstract: We extend Green-relations from usual semigroups to (n,m)-semigroups. We further define broad (n,m)-semigroups, quasi adequate broad (n,m)-semigroups and adequate broad (n,m)-semigroups and address their fundamental properties.

Key words: (n,m)-semigroup, adequate broad (n,m)-semigroup, quasi adequate broad (n,m)-semigroup, Greenrelations, broad (n,m)-semigroup