  We investigate the Universe evolution at late-time stages in models of
teleparallel gravity with power-law nonminimal coupling and a decreasing
power-law potential of the scalar field $\phi$. New asymptotic solutions are
found analytically for these models in vacuum and with a perfect fluid.
Applying numerical integration, we show that the cosmological evolution leads
to these solutions for some region of the initial conditions, and these
asymptotic regimes are stable with respect to homogeneous variations of the
initial data. The physical sense of the results is discussed.
