We report a detailed study of the ultrasonic damping near the nematic-smectic- A phase transition of terephtal-bis- p-p(')-butylaniline (TBBA). Two mechanisms 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 which is observed up to 15 degrees C from the transition, even though the transition is first order. The other is anisotropic; it appears only in the smectic- A phase, and is associated with the relaxation of the order-parameter modulus.