We report on X-ray, optical, and infrared follow-up observations of GRB 980
703. We detect a previously unknown X-ray source in the GRB error box; assu
ming a power-law decline, we find for its decay index alpha < -0.91 (3 sigm
a). We invoke host-galaxy extinction to match the observed spectral slope w
ith the slope expected from "fireball" models. We find no evidence for a sp
ectral break in the infrared to X-ray spectral range on 1998 July 4.4, and
determine a lower limit of the cooling break frequency, v(c) > 1.3 x 10(17)
Hz. For this epoch we obtain an extinction of A(V) = 1.50 +/- 0.11. From t
he X-ray data we estimate the optical extinction to be A(V) = 20.2(-7.3)(+1
2.3), inconsistent with the former value. Our optical spectra confirm the r
edshift of z = 0.966. We compare the afterglow of GRB 980703 with that of G
RB 970508 and find that the fraction of the energy in the magnetic field, e
psilon(B) < 6 x 10(-5), is much lower in the case of GRB 980703, as a conse
quence of the high frequency of the cooling break.