Oxides RNiO3 (R = rare-earth, R # La) exhibit a metal-insulator (MI) transition at a temperature TMI and an antiferromagnetic (AF) transition at TN. Specific heat (CP) and anelastic spectroscopy measurements were performed in samples of Nd1-xEuxNiO3, 0 <= x <= 0.35. For x = 0, a peak in CP is observed upon cooling and warming at essentially the same temperature TMI = TN ~ 195 K, although the cooling peak is much smaller. For x >= 0.25, differences between cooling and warming curves are negligible, and two well defined peaks are clearly observed: one at lower temperatures, that define TN, and the other one at TMI. An external magnetic field of 9 T had no significant effect on these results. The elastic compliance (s) and the reciprocal of the mechanical quality factor (Q^-1) of NdNiO3, measured upon warming, showed a very sharp peak at essentially the same temperature obtained from CP, and no peak is observed upon cooling. The elastic modulus hardens below TMI much more sharply upon warming, while the cooling and warming curves are reproducible above TMI. On the other hand, for the sample with x = 0.35, s and Q^-1 curves are very similar upon warming and cooling. The results presented here give credence to the proposition that the MI phase transition changes from first to second order with increasing Eu doping.