The mineral monazite, a mixed lanthanide orthophosphate $\mathrm{Ln}\mathrm{P}{\mathrm{O}}_{4}$, is considered as a perfect host for geologic disposal of actinides, rare earths, and possibly other elements formed during nuclear-reactor operation. Synthetic monazite-type orthophosphates of all the elements of the first half of the lanthanide series (except Pm) have been prepared: single crystals were grown using a flux technique, and powders were precipitated in molten urea. The electron-paramagnetic-resonance (EPR) spectra of intentionally added Gd impurities show that the ${\mathrm{Gd}}^{3+}$ ions occupy predominantly substitutional rare-earth sites in both the flux-grown single crystals and the precipitated powders. Though these sites have a very low (triclinic ${C}_{1}$) symmetry, the spectra were successfully interpreted using an orthorhombic spin Hamiltonian. It has been found that, while the main spin-Hamiltonian parameter ${b}_{2}^{0}$ is almost constant when going from the LaP${\mathrm{O}}_{4}$ to the EuP${\mathrm{O}}_{4}$ host (${b}_{2}^{0}\ensuremath{\approx}+830\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$), the parameter ${b}_{2}^{2}$ decreases monotonically from +373 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ to +283 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively. The complete analysis (i.e., angular variations of the EPR lines and position of the principal electric field axes relative to the crystallographic axes) of the EPR single-crystal spectra has been done for the two diamagnetic hosts LaP${\mathrm{O}}_{4}$ and EuP${\mathrm{O}}_{4}$, where the observed EPR lines are the sharpest. It is shown, in particular, that the two magnetically inequivalent EPR spectra (i.e., 14 lines) observed for the monazite-type single crystals are in fact equivalent when the magnetic field is applied parallel or perpendicular to the $b$ axis of the monoclinic structure (i.e., for these directions, only seven degenerate lines are observed). These results are in perfect agreement with the description of the monazite structure whose unit cell contains four "different" rare-earth sites that transform with the symmetry operations of the ${C}_{2h}$ group. The present investigation constitutes an indispensable basis for subsequent studies of actinide-doped monazite orthophosphates or of $\ensuremath{\alpha}$-induced radiation damage in these hosts.