  In this paper we prove and discuss some new $\left(H_{p},weak-L_{p}\right) $
type inequalities of maximal operators of Vilenkin-N\"orlund means with
monotone coefficients. We also apply these results to prove a.e. convergence of
such Vilenkin-N\"orlund means. It is also proved that these results are the
best possible in a special sense. As applications, both some well-known and new
results are pointed out.
