We propose to replace the nonlocal Hartree-Fock exchange in conventional exchange-correlation hybrid functionals by the local exact-expression approximate exchange (EEAX) terms, such as, for example, the self-consistent alpha (SCalpha), the asymptotically-adjusted self-consistent alpha (AASCalpha), the localized Hartree-Fock method introduced by Gorling or the approximation to the optimized effective potential method introduced by Krieger, Li, and Iafrate. Such replacement is justified by the fact that the exchange energy expression of the EEAX functionals is equal to the Hartree-Fock one (exact exchange) while the corresponding EEAX exchange potential is a local, multiplicative operator. Applications to diatomic molecules for the case of EEAX=SCalpha, AASCalpha are presented. The performance of new totally local "hybrid" exchange-correlation functionals is quite close to that of the original nonlocal hybrid models. (C) 2003 American Institute of Physics.