We have investigated, using e.p.r. methods, the effects of X-rays on undoped and hydrogendoped alkaline earth fluorides. We find that irradiation of undoped CaF$_2$ at any temperature does not produce F centres in observable concentration. Irradiation of undoped SrF$_2$ and BaF$_2$ at 77 $^\circ$K produces V$_k$ centres and trapped electron centres which anneal out below room temperature. The undoped SrF$_2$ and BaF$_2$ crystals are extremely difficult to colour with room temperature X-irradiation due, apparently, to recombination of electrons and holes. Irradiation of SrF$_2$:H and BaF$_2$:H crystals at 77 $^\circ$K produces hydrogen atoms in fluorine sites (H$^0_s$ centres) and trapped electron centres. The rate of introduction of the electron centres into the crystals is greater by a factor of about 3 than in the undoped crystals. Irradiation of CaF$_2$:H at 77 $^\circ$K also produces H$^0_s$ centres and trapped electron centres but the rate of generation of the electron centres in these crystals is greater than in undoped CaF$_2$ by a factor of at least 25. The origin of this difference in the behaviour of CaF$_2$:H and the behaviour of SrF$_2$:H and BaF$_2$:H and the nature of the response of alkaline earth fluorides to X-rays are discussed. The use of polarized bleaching light to extract information from the optical absorption spectrum of irradiated CaF$_2$:H is described in an appendix.