Summary: This paper deals with the inequalities involving the Schwab-Borchardt mean and other bivariate means including those introduced by

*H.-J. Seiffert* in [Problem 887, Nieuw Arch. Wisk 11, p. 176 (1993) and Aufgabe 16, Wurzel 29, p. 87 (1995)]. The main results of this paper are obtained using a representation of the Schwab-Borchardt mean in terms of the

$R$-hypergeometric functions of two variables. The Ky Fan type inequalities for the particular means contained in the family of the Schwab-Borchardt means are also included. See also Part I by the same authors [Math. Pannonica 14, No. 2, 253–266 (2003;

Zbl 1053.26015)].