The present study demonstrates, by means of broadband dielectric measurements, that the primary α- and the secondary Johari-Goldstein (JG) β-processes are strongly correlated, in contrast with the widespread opinion of statistical independence of these processes. This occurs for different glass-forming systems, over a wide temperature and pressure range. In fact, we found that the ratio of the α- and β- relaxation times is invariant when calculated at different combinations of P and T that maintain either the primary or the JG relaxation times constant. The α-β interdependence is quantitatively confirmed by the clear dynamic scenario of two master curves (one for α-, one for β-relaxation) obtained when different isothermal and isobaric data are plotted together versus the reduced variable T g (P)/T, where T g is the glass transition temperature. Additionally, the α-β mutual dependence is confirmed by the overall superposition of spectra measured at different T-P combinations but with an invariant α-relaxation time.