  The main purpose of the paper is to present some powerful data on the
advantage of the rational approximation procedure based on Hermite-Pad\'e
polynomials over the Pad\'e approximation procedure. The first part of the
paper is devoted to some numerical examples in this direction. The second part
will be devoted to some theoretical results. In particular, we demonstrate our
ideas about the advantage of rational Hermite-Pad\'e approximants over Pad\'e
approximants analyzing the analytical structure of the frequency function $\nu$
of the free Van der Pol equation.
