  We study the asymptotic behavior of Multiple Meixner polynomials of first and
second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153,
(2003)). We use an algebraic function formulation for the solution of the
equilibrium problem with constrain to describe their zero distribution. Then
analyzing the limiting behavior of the coefficients of the recurrence relations
for Multiple Meixner polynomials we obtain the main term of their asymptotics.
