The compounds UCuOP and NpCuOP have been synthesized and their crystal structures were determined from low-temperature single-crystal X-ray data. These isostructural compounds crystallize with two formula units in space group P4/nmm of the tetragonal system. Each An atom (An = U or Np) is coordinated to four O and four P atoms in a distorted square antiprism; each Cu atom is coordinated to four P atoms in a distorted tetrahedron. Magnetic susceptibility measurements on crushed single crystals indicate that UCuOP orders antiferromagnetically at 224(2) K. Neutron diffraction experiments at 100 and 228 K show the magnetic structure of UCuOP to be type AFI (+ - + -) where ferromagnetically aligned sheets of U atoms in the (001) plane order antiferromagnetically along [001]. The electrical conductivity of UCuOP exhibits metallic character. Its electrical resistivity measured in the ordered region with he current flowing within the tetragonal plane is governed by the scattering of the conduction electrons on antiferromagnetic spin-wave excitations. The electrical resistivity of single-crystalline NpCuOP shows semimetallic character. It 5 dominated by a pronounced hump at low temperatures, which likely arises owing to long-range magnetic ordering below about 90 K. Density of state analyses using the local spin-density approximation show covalent overlap between AnO and CuP layers of the structure and dominant contributions from 5f-actinide orbitals at the Fermi level. Calculations on a 2 x 2 x 2 supercell of NpCuOP show ferromagnetic ordering within the Np sheets and complex coupling between these planes. Comparisons of the physical properties of these AnCuOP compounds are made with those of the family of related tetragonal uranium phosphide compounds.