In this paper, we discuss the possibility of theoretical exploration of moral dilemmas as well as the elaboration the solution strategy from the standpoint of the deontological ethics. The main difficulties the deontological ethics in this area are identified. Hereafter we analyze the main provisions of the moral doctrine of I. Kant, who is usually regarded as the main authority for strict deontological position in ethics. We try to prove that it is not the categorical imperative, but the «‘ought’ implies ‘can’» principle should be considered as the starting point for the analysis of moral dilemmas in Kantian deontology, taking into consideration that Kant himself claimed the conflict of duties to be fundamentally impossible. We suggest that the modifying the basic principles of deontology would allow it to explore moral dilemmas. The most effective modification would be that comprises the concept of responsibility without sacrificing the «‘ought’ implies ‘can’» principle. At the same time, there is no necessity to construct a moderate version of deontology with the ranking of moral responsibilities. So we analytically discuss the closest theoretical positions of H. Jonas who modified the Kantian moral requirement, showing its anthropological limitations. The role the prediction of the technological development consequences plays the principle of responsibility by H. Jonas is shown. R. Barkan Marcus focuses attention on the unanticipated character of the moral dilemmas that may interfere with the implementation of the postulates of practical reason. She develops the concept of duty, aimed at providing certain condition that will facilitate the performance of moral acts in the future.