The Low Earth Orbit (LEO) satellites are nowadays not only used for purposes of communications, remote sensing and scientific research, their functions in augmenting the Global Navigation Satellite Systems (GNSSs) in the Positioning, Navigation and Timing (PNT) services have been discussed in recent years. Due to their much lower orbital heights than the GNSS satellites, they have shown great benefits in providing a much stronger signal strength, accelerating the change of the measurement geometry, and greatly increasing the visibility in GNSS-challenging areas. To facilitate real-time ground-based positioning, the LEO satellite orbits need to be predicted. Depending on the latencies of the real-time LEO satellite orbits, the predicted orbits of different periods will be used, where the prediction errors are closely related to the prediction periods themselves. While the LEO satellite orbit prediction has been studied mainly for prediction periods of a few hours, this study concentrates on extreme cases, i.e., very short prediction within 10 min and very long prediction from 12 h to 7 days. Using LEO satellites GRACE C and Sentinel-3B of about 500 and 800 km, respectively, the prediction strategies and prediction errors are discussed for these very short and very long predictions. It was found that the RMS of the global averaged Orbital User Range Errors (OUREs) is about 2 cm at the prediction time of 10 min for both test satellites, when setting the corresponding fitting interval to 2 h and the interval between subsequent stochastic velocity pulses to 30 min to 1 h. For long-term predictions of a few days, no velocity pulse is considered in the prediction. The long-term prediction errors are highly correlated with the orbital heights, and are dominated by the along-track prediction errors due to the air drag influences. When applying appropriate fitting times, the RMS of the OURE at a prediction time of 7 days is about 43 m for the 800 km Sentinel-3B, while it increases to about 616 m for the 500 km GRACE C.