A space X has the ΩEP-property if for each self-mapping the set of nonwandering points is contained in the closure of the set of eventually periodic points. A class of λ-dendroids is presented each member of which has the ΩEP-property for mappings satisfying certain additional conditions. These λ-dendroids are obtained as compactifications of some dendrites without finite sets. Some related problems are posed.