Abstract: High resolution birefringence measurements and Modulated Differential Scanning Calorimetry have been carried out in order to investigate the critical behaviour near the Isotropic to Smectic-A, Smectic-A to Smectic-C_a* phase transitions associated with two well known antiferroelectric liquid crystalline materials R- and S-enantiomers of MHPOBC [4-(1-methylheptyloxycarbonyl) phenyl 4¢-octyloxybiphenyl-4-carboxylate] and their racemic mixture. The heat capacity anomaly and the birefringence data serve as order parameter and the critical exponents extracted from these order parameters corresponding to the various transitions associated with the investigated materials indicates the nature of the transition whether it is first order or second order. The data have been analyzed in detail with the renormalization-group expression with correction-to-scaling terms. A comparison of specific heat-capacity critical exponent found from the mean-square fluctuations of the tilt angle <δq²(T)> and the critical exponent (α′) explored from the birefringence differential quotient Q (T) for the SmA-SmC_a* phase transition has also been done for pure R-MHPOBC and S-MHPOBC. The nature of phase transition associated with the racemic mixture of MHPOBC has also been discussed in the light of precise birefringence and specific heat capacity measurements.