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There is an ongoing effort to design optimal intervention strategies for discrete state-space synchronous genetic regulatory networks in the context of probabilistic Boolean networks; however, to date, there has been no corresponding effort for asynchronous networks. This paper addresses this issue by postulating two asynchronous extensions of probabilistic Boolean networks and developing control policies for both. The first extension introduces deterministic gene-level asynchronism into the constituent Boolean networks of the probabilistic Boolean network, thereby providing the ability to cope with temporal context sensitivity. The second extension introduces asynchronism at the level of the gene activity profiles. Whereas control policies for both standard probabilistic Boolean networks and the first proposed extension are characterized within the framework of Markov decision processes, asynchronism at the profile level results in control being treated in the framework of semi-Markov decision processes. The advantage of the second model is the ability to obtain the necessary timing information from sequences of gene-activity profile measurements. Results from the theory of stochastic control are leveraged to determine optimal intervention strategies for each class of proposed asynchronous regulatory networks, the objective being to reduce the time duration that the system spends in undesirable states.