A semigroup S with a unary operation \(x\to x^*\) is called a regular *- semigroup if it satisfies (i) \((x^*)^*=x\); (ii) \((xy)^*=y^*x^*\); and (iii) \(xx^*x=x\). Firstly, antiautomorphisms and involutions of Rees matrix semigroups are studied. These results are used to investigate varieties of completely simple *-semigroups. Next, regular *-semigroups which are also normal bands of groups are characterized. By using this result, some of their varieties are studied. Finally, the variety determined by the identity \(axa^*a=aa^*xa\) is characterized. The results for varieties of regular *-semigroups in this paper are analogous to the results of the author [Can. J. Math. 29, 1171- 1197 (1977; Zbl 0342.20029)] given for varieties of completely regular semigroups.