We report on X-ray , optical and infrared follow-up observations of GRB 980703 . We detect a previously unknown X-ray source in the GRB error box ; assuming a power law decline we find for its decay index \alpha < –0.91 ( 3 \sigma ) . We invoke host galaxy extinction to match the observed spectral slope with the slope expected from ‘ fireball ’ models . We find no evidence for a spectral break in the infrared to X-ray spectral range on 1998 July 4.4 , and determine a lower limit of the cooling break frequency : \nu _ { c } > 1.3 \times 10 ^ { 17 } Hz . For this epoch we obtain an extinction of A _ { V } = 1.50 \pm 0.11 . From the X-ray data we estimate the optical extinction to be A _ { V } = 20.2 ^ { +12.3 } _ { -7.3 } , inconsistent with the former value . Our optical spectra confirm the redshift of z =0.966 found by Djorgovski et al . ( 1998 ) . We compare the afterglow of GRB 980703 with that of GRB 970508 and find that the fraction of the energy in the magnetic field , \epsilon _ { B } < 6 \times 10 ^ { -5 } , is much lower in the case of GRB 980703 , which is a consequence of the high frequency of the cooling break .