With the modernization of GPS and the deployment of GALILEO, multiple frequencies will be available for civil users from both systems. The two systems will provide about twice the number of satellites compared to the current GPS; thus a significant number of ambiguities will be required to be resolved in dual system multifrequency carrier phase positioning. Previous studies had shown that the probability of correct fix (PCF) of ambiguities decreases with an increase in the number of ambiguities; it should be much harder to fix all the ambiguities within the multiple frequencies in the GPS/GALILEO combined system. As an option to overcome this, partial integer ambiguity fixing was adopted in this paper to investigate the characteristics of fixing a subset of ambiguities. Various scenarios of ambiguity resolution in independent GPS, independent GALILEO and their combination are considered in simulation. Numerical results show, as expected, that the PCF of ambiguities does decrease as the number of ambiguities increases, while the positioning accuracy improves as more and more ambiguities are resolved. Interestingly, it is shown that a 30 satellite GPS constellation outperforms the 30 satellite GALILEO constellation with the same number of satellites observed for high latitude users. In terms of the combination of GPS and GALILEO, higher levels of PCF and higher positioning accuracies can be obtained in shorter time compared to using each system independently.