Abstract: The AX-PET collaboration has developed a novel concept for high resolution PET imaging to overcome some of the performance limitations of classical PET cameras, in particular the compromise between spatial resolution and sensitivity introduced by the parallax error. The detector consists of an arrangement of long LYSO scintillating crystals axially oriented around the field of view together with arrays of wave length shifter strips orthogonal to the crystals. This matrix allows a precise 3D measurement of the photon interaction point. This is valid both for photoelectric absorption at 511 key and for Compton scattering down to deposited energies of about 100 keV. Crystals and WLS strips are individually read out using Geiger-mode Avalanche Photo Diodes (G-APDs). The sensitivity of such a detector can be adjusted by changing the number of layers and the resolution is defined by the crystal and strip dimensions. Two AX-PET modules were built and fully characterized in dedicated test set-ups at CERN, with point-like Na-22 sources. Their performance in terms of energy (Renew approximate to 11.8% (FWMH) at 511 key) and spatial resolution was assessed (sigma(axial) approximate to 0.65 mm), both individually and for the two modules in coincidence. Test campaigns at ETH Zurich and at the company AAA allowed the tomographic reconstructions of more complex phantoms validating the 3D reconstruction algorithms. The concept of the AX-PET modules will be presented together with some characterization results. We describe a count rate model which allows to optimize the planing of the tomographic scans.