Local linear stability of swept and unswept incompressible boundary layers developing over compliant, fluid-saturated, porous plates is considered in the limit of small permeability. The analysis is meant to yield preliminary indications on the possible stabilization induced on the flow's hydrodynamic and hydroelastic modes by poroelastic media, such as those occurring in many natural and technological settings. As far as hydrodynamic modes are concerned, the main stabilizing effect is that of compliance, which however couples weakly to low-frequency crossflow modes. Permeability plays a damping role on hydroelastic modes, which here take the form of travelling wave flutter instabilities. The passive control of instabilities through poroelastic coatings specifically designed to selectively exploit the effect of compliance and/or permeability is a subject worthy of future research efforts.