We study the possibility to obtain high-intensity pulses that maintain a constant Carrier Envelope Phase (CEP) during propagation in dispersive media, i.e. pulses such that the carrier-wave offset with respect to the main intensity peak remains fixed. Our numerical experiments strongly suggest that pulse splitting and X-wave formation within femtosecond laser pulse filamentation leads to the formation of "constant-CEP" within well-defined regions inside the filament. We study the creation of "constant-CEP" pulses in both gasseous and condensed media showing that this is a generic feature of filaments. (C) 2008 Optical Society of America.