  We study two types of simple Boolean networks, namely two loops with a
cross-link and one loop with an additional internal link. Such networks occur
as relevant components of critical K=2 Kauffman networks. We determine mostly
analytically the numbers and lengths of cycles of these networks and find many
of the features that have been observed in Kauffman networks. In particular,
the mean number and length of cycles can diverge faster than any power law.
