  The $\Delta$-excitation in $\overline{p}d$ annihilation at rest was studied.
The annihilation amplitude from the statistical model and the $\pi N$ amplitude
from the resonance model were adopted in our calculations. We analyze the
invariant mass of the $\pi^+p$ and $\pi^-p$ systems selecting the protons with
momenta above 400 MeV/c and with respect to the different final reaction
channels. Our model reproduces reasonably the experimental data.
