Testing is usually understood to involve the tester interacting with the studied system by supplying input and observing output. However, sometimes this active interaction is not possible and testing becomes more passive. In this setting, passive testing can be considered to be the process of checking that the observations made regarding the system satisfy certain required properties. In this paper we study a formal passive testing framework for systems where there is an asynchronous communications channel between the tester and the system. We consider a syntactic definition of a class of properties and provide a semantic representation, as automata, that take into account the different observations that we can expect due to the assumption of asynchrony. Our solution checks properties against traces in polynomial time, with a low need for storage. Therefore, our proposal is very suitable for real-time passive testing.