An experimental study of acoustic emission (AE) in a single crystal and in a polycrystalline sample of Fe68.8Pd31.2 is presented. The samples are studied in a temperature range that is known to include not only a martensitic transition (MT) but also premartensitic effects and strong lattice-parameter variations below the transition. AE activity is compared to calorimetric and magnetic-susceptibility measurements. AE has only been detected during the martensitic transition. The kinetics of the MT for the single crystal exhibits a series of reproducible peaks of activity. This structured activity is not observed for the polycrystal, which shows a single-peak behavior. Despite these differences the AE measurements reveal that the martensitic transitions in both samples start at the same temperature. Results are also compatible with a negligible hysteresis at the transition. The statistics of the amplitude, energy, and duration of AE signals is analyzed in detail and characterized by power-law exponents. For the single crystal the exponents are coincident for heating and cooling ramps and are independent of the rate. For the polycrystalline sample, the exponents are different for heating and cooling.