The formation of nanovoids in Si(100) and MgO(100) by 3He ion implantation has been studied. Contrary to Si in which the voids are generally almost spherical, in MgO nearly perfectly rectangular nanosize voids are created. Recently, the 2D-ACAR setup at the Delft Positron Research Center has been coupled to the intense reactor-based variable-energy positron beam POSH. This allows a new method of monitoring thin layers containing nanovoids or defects by depth-selective high-resolution positron beam analysis. The 2D-ACAR spectra of Si with a buried layer of nanocavities reveal the presence of two additional components, the first related to para-positronium (p-Ps) formation in the nanovoids, and a second one most likely related to unsaturated Si-bonds at the internal surface of the voids. The positronium is present in excited kinetic states with an average energy of 0.3 eV. Refilling of the cavities by means of low dose 3He implantation (1×1014 cm-2) followed by annealing reduces the formation of Ps and the width of the Ps peak in the ACAR spectrum. This width reduction is due to collisions of Ps with He atoms in the voids. In MgO, p-Ps formed with an initial energy of ∼3 eV shows a final average energy of 1.6 eV at annihilation due to collisions with the cavity walls. Possibilities of this new, non-destructive method of monitoring the sizes of cavities and the evolution of nanovoid layers will be discussed.