The concept of weakly quasiadequate semigroups was introducted.It is a kind of semigoup intervening between abundant semigroup and adequate semigroup.The properties and structure of such a semigroup without zero with a multiplicative adequate transversal were investigated.It is concluded that the condition of equivalence is that the abundant semigroup with a multiplicative adequate transversal is the weakly quasiadequate semigroups.