Measurements were made to check the performance of the CERN high intensity RFQs (RFQ2A and RFQ2B) and assess the validity of the design approach; the study of space charge effects was undertaken in this context. RFQ2A and RFQ2B are 200 mA, 750 keV proton accelerators, operating at 202.56 MHz. Since the beginning of 1993, RFQ2B serves as injector to the CERN 50 MeV Alvarez linac (Linac 2). In 1992, both RFQs were on the test stand to undergo a series of beam measurements, which were compared with computations. The studies concerning the RFQ2A were more detailed and they are reported in this paper. ©1996 American Institute of Physics.