Two modules of the AD detector have been studied with the test beam at the T10 facility at CERN. The AD detector is made of scintillator pads read out by wave-length shifters (WLS) coupled to clean fibres that carry the produced light to photo-multiplier tubes (PMTs). In ALICE the AD is used to trigger and study the physics of diffractive and ultra-peripheral collisions as well as for a variety of technical tasks like beam-gas background monitoring or as a luminometer. The position dependence of the modules' efficiency has been measured and the effect of hits on the WLS or PMTs has been evaluated. The charge deposited by pions and protons has been measured at different momenta of the test beam. The time resolution is determined as a function of the deposited charge. These results are important ingredients to better understand the AD detector, to benchmark the corresponding simulations, and very importantly they served as a baseline for a similar device, the Forward Diffractive Detector (FDD), being currently built and that will be in operation in ALICE during the LHC Runs 3 and 4.