  We investigate commensurability classes of hyperbolic knot complements in the
generic case of knots without hidden symmetries. We show that such knot
complements which are commensurable are cyclically commensurable, and that
there are at most $3$ hyperbolic knot complements in a cyclic commensurability
class. Moreover if two hyperbolic knots have cyclically commensurable
complements, then they are fibered with the same genus and are chiral. A
characterisation of cyclic commensurability classes of complements of periodic
knots is also given. In the non-periodic case, we reduce the characterisation
of cyclic commensurability classes to a generalization of the Berge conjecture.
