  We calculate the axial $N\to \Delta(1232)$ and $N\to N^{\star}(1440)$
transition form factors in a chiral constituent quark model. As required by the
partial conservation of axial current ($PCAC$) condition, we include one- and
two-body axial exchange currents. For the axial $N\to \Delta(1232)$ form
factors we compare with previous quark model calculations that use only
one-body axial currents, and with experimental analyses. The paper provides the
first calculation of all weak axial $N\to N^{\star}(1440)$ form factors. Our
main result is that exchange currents are very important for certain axial
transition form factors. In addition to improving our understanding of nucleon
structure, the present results are relevant for neutrino-nucleus scattering
cross section predictions needed in the analysis of neutrino mixing
experiments.
