In the present work, a detailed analysis of the glassy behavior and the relaxation dynamics of the liquid crystal dimer a-(4-cyanobiphenyl-4'-yloxy)-¿-(1-pyrenimine-benzylidene-4'-oxy) heptane (CBO7O.Py) throughout both nematic and smectic-A mesophases by means of broadband dielectric spectroscopy has been performed. CBO7O.Py shows three different dielectric relaxation modes and two glass transition (Tg) temperatures: The higher Tg is due to the freezing of the molecular motions responsible for the relaxation mode with the lowest frequency (µ1L); the lower Tg is due to the motions responsible for the two relaxation modes with highest frequencies (µ1H and µ2), which converge just at their corresponding Tg. It is shown how the three modes follow a critical-like description via the dynamic scaling model. The two modes with lowest frequencies (µ1L and µ1H) are cooperative in the whole range of the mesophases, whereas the highest frequency mode (µ2) is cooperative just below some crossover temperature. In terms of fragility, at the glass transition, the ensemble (µ1H+µ2) presents a value of the steepness index and µ1L a different one, meaning that fragility is a property intrinsic to the molecular motion itself. Finally, the steepness index seems to have a universal behavior with temperature for the dielectric relaxation modes of liquid crystal dimers, being almost constant at high temperatures and increasing drastically when cooling the compound down to the glass transition from a temperature about 34TNI.