  The classical notion of {\L}ojasiewicz ideals of smooth functions is studied
in the context of non-quasianalytic Denjoy-Carleman classes. In the case of
principal ideals, we obtain a characterization of {\L}ojasiewicz ideals in
terms of properties of a generator. This characterization involves a certain
type of estimates that differ from the usual {\L}ojasiewicz inequality. We then
show that basic properties of {\L}ojasiewicz ideals in the $\mathcal{C}^\infty$
case have a Denjoy-Carleman counterpart.
