Let G = (V, E), V = {v1, v2, …, vn }, be a simple connected graph of order n and size m. Denote by (Formula presented) the normalized signless Laplacian eigenvalues of G, and by σα (G) the sum of α-th powers of the normalized signless Laplacian eigenvalues of a connected graph. The paper deals with bounds of σα. Some special cases, when (Formula presented) are also considered.