Galileo, the European global navigation satellite system, is in its in-orbit validation phase and the four satellites which have been available for some months now have allowed a preliminary analysis of the system performance. Previous studies have showed that Galileo will be able to provide pseudorange measurements more accurate than those provided by GPS. However, a similar improvement was not found for pseudorange rate observations in the velocity domain. This fact stimulated additional analysis of the velocity domain, and, in particular, an unintended oscillatory component was identified as the main error source in the velocity solution. The magnitude of such oscillation is less than 10 cm/s, and its period is in the order of few minutes. A methodology was developed to identify oscillatory components in the Galileo IOV pseudorange rate observables, and it was verified that the measurements from Galileo IOV PFM and Galileo IOV FM2 are affected by a small oscillatory disturbance. This disturbance stems from the architecture adopted for combining the frequency references provided by the two active clocks present in the Galileo satellites. The issue has been solved in Galileo IOV FM3 and Galileo IOV FM4, and the oscillatory component has been eliminated. We also propose a methodology for removing this unwanted component from the final velocity solution and for determining the performance that Galileo will be able to achieve. The analysis shows that Galileo velocity solution will provide a root-mean-square error of about 8 cm/s even in the limited geometry conditions achieved using only four satellites. This shows the potential of Galileo also in the determination of user velocity.