  We propose the class of galled tree-child networks which is obtained as
intersection of the classes of galled networks and tree-child networks. For the
latter two classes, (asymptotic) counting results and stochastic results have
been proved with very different methods. We show that a counting result for the
class of galled tree-child networks follows with similar tools as used for
galled networks, however, the result has a similar pattern as the one for
tree-child networks. In addition, we also consider the (suitably scaled)
numbers of reticulation nodes of random galled tree-child networks and show
that they are asymptotically normal distributed. This is in contrast to the
limit laws of the corresponding quantities for galled networks and tree-child
networks which have been both shown to be discrete.
