We study the hydrodynamical behavior of the gas expelled by moving Asymptotic Giant Branch Stars interacting with the ISM . Our models follow the wind modulations prescribed by stellar evolution calculations , and we cover a range of expected relative velocities ( 10 to 100 km s ^ { -1 } ) , ISM densities ( between 0.01 and 1 { cm } ^ { -3 } ) , and stellar progenitor masses ( 1 and 3.5M _ { \odot } ) . We show how and when bow-shocks , and cometary-like structures form , and in which regime the shells are subject to instabilities . Finally , we analyze the results of the simulations in terms of the different kinematical stellar populations expected in the Galaxy .