In Washington D.C., on 25 January 1999, Vice President Al Gore announced that two new civil signals would be broadcast on future Block IIF GPS satellites. These new civilian signals, in combination with the L1 signal now available, will greatly enhance the accuracy, reliability and robustness of civilian GPS receivers, resulting in significantly improved system capabilities. This improved GPS performance will have a tremendous impact on navigation, positioning and timing services, but especially for high accuracy users engaged in surveying, geodesy, atmospheric monitoring, etc., who make use of GPS carrier phase measurements. The mathematical process that converts ambiguous carrier phase measurements to unambiguous ranges of millimetre measurement precision, referred as Ambiguity Resolution (AR), is a critical requirement for high accuracy positioning. AR techniques will be significantly impacted upon were two additional civilian frequencies to become available. In this paper, the AR strategies that take advantage of carrier phase measurements on the second and third signal frequencies will be discussed. The linear combination theory of carrier phase measurements will be extended, and following error analysis, several new combination measurements which have longer effective wavelength and less "noise" will be proposed. The new measurement combinations provide an opportunity to resolve double-differenced integer ambiguities using pseudo-range observations directly and with almost no baseline length constraints. Although the new signals are planned only for the Block IIF satellites, and the service will not be available before 2005, the AR strategies described in this paper may be useful for planning purposes, particularly in regard to new applications that may be addressed by lower cost, multiple frequency GPS user technology in the early years of the 21st century.