  For a domain $D$ of $\mathbb{C}^n$ which is weakly $q$-pseudoconvex or
$q$-pseudoconcave we give a sufficient condition for subelliptic estimates for
the $\bar{\partial}$-Neumann problem. The paper extends to domains which are
not necessarily pseudoconvex, the results and the techniques of Catlin.
  MSC: 32D10, 32U05, 32V25
