Quantum-cascade lasers (QCLs) are critical components for high-resolution terahertz spectroscopy, especially in heterodyne spectrometers, where they serve as local oscillators. For this purpose, QCLs with stable frequencies and narrow linewidths are essential since their spectral properties limit the spectral resolution. We demonstrate the phase locking of QCLs around 3.5 and 4.7 THz in mechanical cryocoolers. These frequencies are particularly interesting for atmospheric research because they correspond to the hydroxyl radical and the neutral oxygen atom. The phase-locked loop is based on frequency mixing of the QCLs at 3.5 and 4.7 THz with the sixth and eighth harmonic, respectively, generated by an amplifier-multiplier chain operating around 600 GHz, with a Schottky-diode harmonic mixer. At both frequencies, we achieved a linewidth of the intermediate frequency signal of less than 1 Hz. This is about seven orders of magnitude less than the linewidth of the free-running QCL.