  We show that the polyhomogeneity at infinity of an asymptotically complex
hyperbolic metric is preserved along the Ricci-DeTurck flow. Moreover, if the
initial metric is `smooth up to the boundary', this will be preserved by the
Ricci-DeTurck flow and the normalized Ricci flow. When the initial metric is
K\"ahler, sharper results are obtained in terms of a potential.
