By manipulating Euler factors in a natural way the author proves some identities and congruences connecting the generalized (in Berger-Leopoldt sense) Bernoulli numbers and the p-adic L-functions of Kubota-Leopoldt (for the necessary definitions see \textit{L. C. Washington} [Introduction to cyclotomic fields (Graduate Texts in Math. 83) (Springer 1982; Zbl 0484.12001)]). It was demonstrated, too, for the series of congruences analogous to the known Voronoi and Kummer ones for the ordinary Bernoulli and Euler numbers. This gives a possibility to obtain the approximation of p-adic L-functions by means of the function [x], where [x] is the greatest integer in x. \(\{\) Reviewer's remark: Some preliminary results of that kind were obtained by \textit{J. Fresnel} [Théor. des Nombres, Sémin. Delange- Pisot-Poitou, Fac. Sci. Paris 1964/65, 6, fasc. 2, No.14, 1-12 (1967; Zbl 0206.336)] and the reviewer [Izv. Vyssh. Uchebn. Zaved., Mat. 1972, No.3, 61-69 (1972; Zbl 0244.12006); ibid. 1966, No.4, 118-126 (1966; Zbl 0146.278)]\(\}\).