The M2XO4-type crystals where M=K, Rb, Cs, NH4, Tl; X= S, Se have interesting characteristics, for example ferroelectricity, ferroelasticity and incommensurate modification. These crystals crystallize to an orthorhombic system with the space group Pnam at room temperature. K2SeO4 shows ferroelectricity along the c axis below 93K and ferroelasticity below 745K. Moreover, this crystal has an incommensurate modification along the a axis in the temperature range between 93K and 130K. On the other hand, (NH4)2SO4 shows ferroelectricity below 223K and ferroelasticity at room temperature. 4) However, an incommensurate modification in (NH4)2SO4 was not observed in contrast with K2SeO4. Thallium selenate Tl2SeO4, where the M-site is replaced by thallium, undergoes an improper ferroelastic phase transition at 661K. 6) This ferroelastic one is characterized by the symmetry change from the hexagonal space group P63/mmc to the orthorhombic Pnam in common with many other crystals of a M2XO4 type. Moreover, it has been found by Unrch that Tl2SeO4 undergoes a phase transition at 70K on cooling and at 75K on warming, accompanied by a discontinuous change in the dielectric constant and a thermal hysteresis of 5K which are indicative of first order. The space group of Tl2SeO4 below the phase transition temperature of 70K was reported to be P212121, 8) which is clearly different from the space group Pna21 in the cases of the K2SeO4 and (NH4)2SO4 crystals. Although the M2XO4-type crystals exhibit a common nature in the mechanism of ferroelasticity, a variety of different phase transition has been reported for some of them below room temperature. Recently we examined the thermal property and the spin-lattice relaxation time T1 by means of NMR spectrometer for the Tl2SeO4 crystal, and found a new phase transition at 97K, except for the phase transitions at 70K and 661K. The present paper reports the results obtained for the specific heat and the temperature dependence of T1 for Tl2SeO4 Single crystals Tl2SeO4 were grown by a slow evaporation method at 303K from an aqueous solution of thallium selenate. The single crystals thus grown are of pseudo-hexagonal plate with the predominant (100) faces and are transparent. The specific heat was measured with an AC calorimetric apparatus (ACC-1, Ulvac