Let \(R\) be a ring with identity. \(R\) is said to be semi-commutative if \(xy=0\) implies \(xRy=0\) for \(x,y\in R\). \(R\) is called strongly regular if for each \(a\in R\) there exists \(b\in R\) such that \(a=a^2b\). Some necessary and sufficient conditions for rings to be strongly regular are considered. In particular, the author proves that the following conditions are equivalent: (1) \(R\) is a strongly regular ring; (2) \(R\) is a semicommutative and regular ring; (3) \(R\) is a semicommutative left \(SF\)-ring; (4) \(R\) is a semicommutative ELT ring whose simple left \(R\)- modules are either \(P\)-injective or flat; (5) \(R\) is a semicommutative right nonsingular left \(P\)-injective ring; (6) \(R\) is a semiprime semicommutative left (or right) \(P\)-injective ring.