Development of Kelvin–Helmholtz (KH) instability in solar coronal jets can trigger the wave turbulence considered as one of the main mechanisms of coronal heating. In this review, we have investigated the propagation of normal MHD modes running on three X-ray jets modeling them as untwisted and slightly twisted moving cylindrical flux tubes. The basic physical parameters of the jets are temperatures in the range of 5.2–8.2 MK, particle number densities of the order of cm−3, and speeds of 385, 437, and 532 km s−1, respectively. For small density contrast between the environment and a given jet, as well as at ambient coronal temperature of 2.0 MK and magnetic field around 7 G, we have obtained that the kink () mode propagating on moving untwisted flux tubes can become unstable in the first and second jets at flow speeds of ≅348 and 429 km s−1, respectively. The KH instability onset in the third jet requires a speed of ≅826 km s−1, higher than the observed one. The same mode, propagating in weakly twisted flux tubes, becomes unstable at flow speeds of ≅361 km s−1 for the first and of 443 km s−1 for the second jet. Except the kink mode, the twisted moving flux tube supports the propagation of higher () MHD modes that can become unstable at accessible jets’ speeds.