Scintillation theory is used to study the fading of radio waves returned from the ionospheric F-region in the HF band at oblique incidence. For both low and high penetration frequencies calculations are made as a function of wave frequency, but emphasis is given to behaviour near the maximum usable frequency for one-hop F-transmission over distances up to 4000 km. Estimates are made of 1. (i) the fluctuations of phase both for long-term (~ 1h) and for short-term (~ the fading correlation time), 2. (ii) the fading correlation distance, 3. (iii) the quasi-period of fading, 4. (iv) the twinkling correlation distance, 5. (v) the quasi-period of twinkling, 6. (vi) the angular departure of the arrival azimuth from the mean and 7. (vii) the correlation bandwidth. The slow fluctuations often experienced in long distance HF radio communications are a manifestation of twinkling, rather than fading. Under normal conditions in the F-region the correlation bandwidth is so large that the bandwidth of transmission at HF is controlled by the dispersive properties of the ionosphere, rather than by the scattering properties. The reverse is true in the presence of spread-F. For sufficiently strong spread-F the correlation bandwidth for long distance HF radio communications is of the order of only 10 Hz, thereby creating the phenomenon known as flutter fading. Theoretical estimates of the scintillation parameters are compared with experience in long distance HF ionospheric communications over the last 60 years. Agreement is promising, but future experiments should be designed in the light of theory; existing observational data do not provide some of the information needed.