The molar heat capacities of ammonium hydrogen oxalate hemihydrate and its fully-deuterated compound were measured from 13 to 300 K. A higher-order phase transition was found in each compound. The temperatures and molar entropies of transition are 145.4 K (6.01 J K −1 mol −1 and 160.1 K (8.23 J K −1 mol −1) in the protonated and deuterated compounds, respectively, where the mole refers to (NH 4HC 2O 4) 2·H 2O or (ND 4DC 2O 4) 2·D 2O. The entropies of the transitions indicate that they are order-disorder transitions, probably related to the ordering of one of the ammonium ions. The pressure coefficient of the transition temperature was calculated by the Ehrenfest relation and the available data of the thermal expansivity of the hydrogenous compound: −2.0 × 10 7 Pa K −1 in good agreement with a reported value −1.9 × 10 7Pa K −1 based on a high pressure experiment.