We report a detailed study of the ultrasonic damping near the nematic-smect
ic-A phase transition of terephtal-bis-p-p'-butylaniline (TBBA). Two mechan
isms contribute to the damping. One is isotropic: it is associated with the
critical fluctuations, and leads to a scaling behavior of the 3D-XY type w
hich is observed up to 15 degrees C from the transition, even though the tr
ansition is first order. The other is anisotropic: it appears only in the s
mectic-A phase, and is associated with the relaxation of the order-paramete
r modulus.