[en] Spin-glass-like behaviour and low-temperature specific heat have been investigated for bulk amorphous Er_xN_100-x, (x=33, 50 and 80) alloys prepared by high-rate direct-current sputtering. The competition between ferromagnetic and antiferromagnetic interactions arising from the exchange fluctuations is negligibly small in this system, in contrast to that in amorphous Er-Cu alloys. The random magnetic anisotropy (RMA) suppresses the ferromagnetic coupling, resulting in a spin-glass-like state. The magnetization per Er atom becomes smaller with increasing Er content owing to the increase in the RMA. At the spin freezing temperature T_f the low-temperature specific heat exhibits a broad maximum, which becomes narrower with the decrease in Er content. It should be noted that the temperature at which the magnetic specific heat of the amorphous Er₃₃Ni₆₇ alloy reaches a maximum value coincides with the T_f determined by the alternating-current magnetic susceptibility measurement. The splitting of the ground state from J=15/2 into a Kramers doublet is caused by the electrostatic field, being accompanied by a Schottky-type specific heat with a linear temperature dependence. The magnetic entropy at T_f is estimated to be about 45-60% of the theoretical value, being much larger than those for crystalline dilute spin-glass systems. Moreover, the plot of the magnetic specific heat versus T³2/ is linear at low temperatures. Therefore, it is considered that a ferromagnetic-like spin wave is excited, although its magnetic structure is not ferromagnetic. (author)