Double-porosity is an important characteristic of microstructure in a large range of geomaterials. It designs porous media with connected fissures/fractures or aggregated soils. The origin of double-porosity can be natural or/and it can result from mechanical, chemical or biological damage. The presence of double-porosity can significantly affect the behaviour of geomaterials. In this paper we provide an experimental evidence of the double-porosity effects by performing laboratory experiments. Series of tracer dispersion experiments (in saturated and unsaturated steady-state water flow conditions) in a physical model of double-porosity geomaterial were carried out. For the comparative purposes , experiments of the same type were also performed in a single-porosity model medium. The results clearly showed that the double-porosity microstructure leads to the non-Fickian behaviour of the tracer (early breakthrough and long tail) in both saturated and unsaturated cases.