  In this paper, we determine the transversal instability of periodic traveling
wave solutions of the generalized Zakharov-Kuznetsov equation in two space
dimensions. Using an adaptation of the arguments in \cite{nikolay} in the
periodic context, it is possible to prove that all positive and one-dimensional
$L-$periodic waves are spectrally (transversally) unstable. In addition, when
periodic sign-changing waves exist, we also obtain the same property when the
associated projection operator defined in the zero mean Sobolev space has only
one negative eigenvalue.
