We present two new exchange–correlation functionals for hybrid Kohn–Sham electronic structure calculations based on the nonseparable functional form introduced recently in the N12 and MN12-L functionals but now with the addition of screened Hartree–Fock exchange. The first functional depends on the density and the density gradient and is called N12-SX; the second functional depends on the density, the density gradient, and the kinetic energy density and is called MN12-SX. Both new functionals include a portion of the Hartree–Fock exchange at short-range, but Hartree–Fock exchange is screened at long range. The accuracies of the two new functionals are compared to those of the recent N12 and MN12-L local functionals to show the effect of adding screened exchange, are compared to the previously best available screened exchange functional, HSE06, and are compared to the best available global-hybrid generalized gradient approximation (GGA) and to a high-performance long-range-corrected meta-GGA.