When it comes to inspections in invasive species management, the literature has shown that there is frequently a tension between economic cost reduction and inspection stringency. As such, we analyze the properties of two probabilistic inspection regimes that are designed to screen arriving ships in a seaport for the presence of one or more deleterious invasive species. In the first regime, the seaport inspector screens arriving ships by using fast (less stringent) and slow (more stringent) protocols. In the second regime, the inspector uses a uniformly stringent protocol with stages. We use the theory of continuous time Markov chains (CTMCs) to delineate both inspection regimes. Next, we derive some key long run performance measures associated with each of these two regimes. Finally, we discuss the implications of our analysis for practical invasive species management.