We have investigated intersubband relaxation in $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ multiple quantum wells using a two-color pump-probe technique in a wide energy range around $800\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ $(1.55\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})$. We have observed not only absorption bleaching signals but also, for the first time, induced absorption signals with an ultrafast and a slow component. Absorption bleaching signals are attributed to a phase space filling of the upper subband and a carrier cooling process in the lower subband, with relaxation times of $140\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ and $300--400\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$, respectively. The ultrafast induced absorption corresponds to the absorption of electrons during intra-subband relaxation and the slow component of $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ corresponds to the carrier cooling process. We have also found that the intrinsic absorption width of highly doped materials is as large as the inhomogeneous width, because the dispersion difference of subbands is enhanced by exchange interaction.