Necessary and sufficient conditions for the functions \(\phi\) and \(\psi\) are given so that for any function f(x) and g(x) of bounded \(\phi\)- respectively \(\psi\)-variation and having no common breakpoints, the Stieltjes integral \(\int^{2\pi}_{0}f(x)dg(x)\) exists i.e. \(\phi\) and \(\psi\) form an S-pair. Also for functions \(\phi\) and \(\psi\) forming an S- pair and satisfying certain conditions a Hölder-type inequality for the modulus of the Stieltjes integral and a Parseval identity involving the Fourier coefficients of the functions f and g are derived as corollaries.