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Herein, some critical aspects related to the acquisition of the future Galileo signals are discussed. In particular, the Alternative Binary Offset Carrier (AItBOC) modulation that will be used by the Galileo satellites to broadcast navigation signals on the E5 band is considered, addressing acquisition issues only partially analyzed in previous works. The implementation of an acquisition section for the AltBOC signals is not straightforward, since several different receiver architectures can be used and remarkable differences are required with respect to the conventional signal processing used in GPS receivers. The main problems that must be handled (risk of false lock, resolution of the search space, and computational burden) are outlined in the following. An innovative technique, called multiresolution acquisition and tailored to the AltBOC signals, is then proposed as an effective solution to previous problems. As demonstrated by means of simulations, this novel strategy can be successfully used in coherent dual-band AltBOC receiver architectures with a feasible implementation complexity and it leads to remarkable advantages in terms of acquisition time.