  We introduce and analyze a hybridizable discontinuous Galerkin (HDG) method
for the dual-porosity-Stokes problem. This coupled problem describes the
interaction between free flow in macrofractures/conduits, governed by the
Stokes equations, and flow in microfractures/matrix, governed by a
dual-porosity model. We prove that the HDG method is strongly conservative,
well-posed, and give an a priori error analysis showing dependence on the
problem parameters. Our theoretical findings are corroborated by numerical
examples
