Abstract Measurements have been made of the low-temperature specific heats of lanthanide metaphosphate glasses R(PO3)3 where R is Gd3+, Dy3+, Pr3+, Sm3+, Eu3+ or La3+. A magnetic contribution to the specific heat of the glasses modified by Gd3+ and Dy3++ has been found in the temperature region below 7K. This magnetic specific heat has a T dependence consistent with the high-temperature tail of a Schottky anomaly. The glass containing Pr3+ ions shows excess contributions to the specific heat and to the low-frequency Raman scattering, which are associated with a very large density of low-lying magnetic excitations. To examine the influence of the topological disorder in the glassy state on the magnetic contributions to the calorimetric characteristics, results are compared and contrasted with those for single-crystal PrP5O14.