Let \(A\) be a commutative ring, let \(A[[X]]\) be the ring of formal power series in a single variable \(X\) over some commutative ring \(A\) and let \(A_ +[[X]]\) be the set of formal power series of \(A[[X]]\) with zero constant term, equipped with its structure of a near-ring obtained with addition and composition. In this paper, the subrings and the subnear- rings of \(A_ +[[X]]\) are studied. One of the main results shows that the subrings of the near-rings \(A_ +[[X]]\) and \(A_ N[[X]]\) (the elements of \(A_ +[[X]]\) whose initial term is nilpotent) are subrings of \(A\).