The tests on the stainless steel prototype for one of the two superconducting RFQs (SRFQs) for PIAVE (SRFQ2), the being built heavy ion injector for the Legnaro booster, were completed in summer 1998, while the construction of the first niobium resonator started in February 1998 and is expected to be completed by April 1999. The structure, resonating at 80 MHz, is 0.8 m long and 0.76 m in diameter. All technological aspects connected with the construction of the SRFQs, and the corresponding tests on the stainless steel model, are reviewed: development of the parts, assembly sequence, electron beam welding (EBW) steps, rough and fine adjustment of the resonant frequency, bead-pull measurements, characterization of the mechanical vibration modes, frequency change due to cooling down and chemical etching tests. The updated development of SRFQ1 is briefly reviewed. ©1999 American Institute of Physics.