We obtain a property of the distribution of the eigenvalues of a quasi-M- matrix and give general estimations for it using results of Wenting Tong [Acta math. Sinica 20, 272-275 (1977; Zbl 0397.15008)] and Jiaju Zhang [Chin. Ann. Math. 1, 47-50 (1980; Zbl 0442.15005)]. We discuss bounds for the smallest eigenvalue, according to modulus, of an M-matrix from other direction, and we give estimations to the bounds of all eigenvalues of an irreducible M-matrix.