A class of exact solutions of Einstein's equations is presented which describes accelerating photon rockets in de Sitter and anti-de Sitter universe. These are particular members of the Robinson-Trautman family of axially symmetric spacetimes with pure radiation. In particular, generalizations of (type D) Kinnersley's rockets and (type II) Bonnor's rockets to the case of a non-vanishing cosmological constant are given. Some of the main physical properties of these solutions are investigated, and their relation to the C-metric solution which describes uniformly accelerated black holes is also given.

8 pages. To appear in Phys. Rev. D