  The existence of the limit distribution of the zeros of Hermite-Pad\'e
polynomials of type II for a pair of functions forming a Nikishin system is
proved using the scalar equilibrium problem posed on the two-sheeted Riemann
surface.
  The relation of the results obtained here to some results of H. Stahl (1988)
is discussed. Results of numerical experiments are presented. The results of
the present paper and those obtained in the earlier paper of the second author
[28], [32], [33] are shown to be in good accordance with both H. Stahl's
results and with results of numerical experiments.
