The proton spin T 1 relaxation dispersion in the smectic A and C phase of TBBA, and for comparison also in the nematic phase, have been studied using time dependent fast field-cycling techniques in the Larmor frequency range from ν p = 100 Hz to 44 MHz. Our measurements considerably extend recent ones by Blinc et al., performed with other NMR methods for frequencies ≧ 140 kHz. The new experimental data are consistent with the reported ones for Sm C but not for Sm A, the difference being that the essential T 1 dispersion observed with our technique occurs at much lower frequencies, namely below about 100 kHz. As a consequence, the relaxation dispersion for both smectic phases looks very similar. It can be described quantitatively in terms of relaxation by "nematic-like" order fluctuations, self-diffusion, and by a third molecular mechanism with (for simplicity) Debve-like power spectrum, which is possibly a second type of order fluctuation or a molecular rotation about the short axis. The analysis reveals surprisingly far going parallels between the spin relaxation of simple smectics and that of high-temperature nematics like PAA.