Asymptotic giant branch stars in the Phoenix dwarf galaxy

JHK(s) near-infrared photometry of stars in the Phoenix dwarf galaxy is presented and discussed. Combining these data with the optical photometry of Massey et al. allows a rather clean separation of field stars from Phoenix members. The discovery of a Mira variable (P = 425 d), which is almost certainly a carbon star, leads to an estimate of the distance modulus of 23.10 +/- 0.18 that is consistent with other estimates and indicates the existence of a significant population of age similar to 2 Gyr. The two carbon stars of Da Costa have M-bol = -3.8 and are consistent with belonging to a population of similar age; some other possible members of such a population are identified. A Da Costa non-carbon star is Delta K-s similar to 0.3 mag brighter than these two carbon stars. It may be an asymptotic giant branch star of the dominant old population. The nature of other stars lying close to it in the K-s, (J - K-s) diagram needs studying.