This paper is devoted to the behavior of the Bergman kernels for almost spherical strictly pseudoconvex domains in C n . We find several first terms of the asymptotics for the Bergman kernel of a strictly pseudoconvex domain with H σ -smooth boundary, 4 < σ < 6. New terms in comparison with the case of C 6 -smooth boundary appear but the growth rate of the remainder remains the same. Bibliography: 16 titles.