We report the behavior of the hexagonal compound CePtPb, which has an antiferromagnetic transition at (Formula presented) K. The magnetic susceptibility is highly anisotropic, with the ratio (Formula presented) extrapolating to the value 65 at (Formula presented). The low-temperature magnetization is also anisotropic with (Formula presented) saturating to (Formula presented) atom at (Formula presented) T, where (Formula presented) is five times smaller. The anisotropy is due both to low-symmetry crystal fields and to exchange anisotropy, which causes basal plane ferromagnetic fluctuations to develop below (Formula presented) K. Three facts suggest that the magnetic order might coexist with heavy-fermion behavior: heat-capacity data show a linear-in-temperature contribution (Formula presented) mJ/mol (Formula presented) in the antiferromagnetic state; the resistivity is quadratic in temperature below (Formula presented); and the magnetic entropy is generated very slowly with temperature reaching a value of only (Formula presented) at (Formula presented). On the other hand, the long high-temperature tail of the heat-capacity data correlates with the ferromagnetic fluctuations above (Formula presented); and ac susceptibility measurements under hydrostatic pressure (to 17 kbar) show that (Formula presented) increases with pressure at an approximate rate 20 mK/kbar, which suggests that CePtPb sits in the small (Formula presented) limit of the Doniach phase diagram; hence heavy-fermion effects may be negligible. © 1996 The American Physical Society.