  In a previous paper, Mihoubi et al. introduced the $(r_{1},...,r_{p})
$-Stirling numbers and the $(r_{1},...,r_{p}) $-Bell polynomials and gave some
of their combinatorial and algebraic properties. These numbers and polynomials
generalize, respectively, the $r$-Stirling numbers of the second kind
introduced by Broder and the $r$-Bell polynomials introduced by Mez\H{o}. In
this paper, we prove that the $(r_{1},...,r_{p}) $-Stirling numbers of the
second kind are log-concave. We also give generating functions and generalized
recurrences related to the $(r_{1},...,r_{p}) $-Bell polynomials.
