We present unique spectroscopic radio observations of comets C/2002 X5 (Kudo-Fujikawa), C/2002 V1 (NEAT), and C/2006 P1 (McNaught), which came within r h ≈ 0.2 AU of the Sun in 2003 and 2007. The molecules OH, HCN, HNC, CS, and CH 3 OH were detected in each of these comets when they were exposed to strong heating from the Sun. HC 3 N and HCO + were detected in comets C/2002 X5 and C/2006 P1, respectively. We show that in these very productive comets close to the Sun screening of the photodissociation by the Sun UV radiation plays a non-negligible role. Acceleration of the gas expansion velocity and day-night asymmetry is also measured and modeled. The CS photodissociation lifetime was constrained to be about 2.5 × 10 −5 s −1 at r h = 1 AU. The relative abundances are compared to values determined from more distant observations of C/2002 X5 or other comets. A high HNC/HCN production-rate ratio, in the range 10-30% between 0.5 and 0.1 AU from the Sun, is measured. The trend for a significant enrichment in CS in cometary comae (CS/HCN ∝ r −0.8 h ) is confirmed in all three comets. The CH 3 OH/HCN production rate ratio decreases at low r h . The HC 3 N/HCN production rate ratio in comet C/2002 X5 is four times higher than measured in any other comet.