Let R be a ring with involution *. An element a ∈ R is called * −strongly regular if there exists a projection p of R such that p ∈ comm 2 (a), ap = 0 and a + p is invertible, and R is said to be * −strongly regular if every element of R is * −strongly regular. We discuss the relations among strongly regular rings, * −strongly regular rings, regular rings and * −regular rings. Also, we show that an element a of a * −ring R is * −strongly regular if and only if a is EP. We finally give some characterizations of EP elements.