Dynamical Response of quasi one-dimensional Mott and CDW insulators. F.H.L. Essler and A.M. Tsvelik Physics Department, Brookhaven National Laboratory, Upton, NY 11973 We calculate the low temperature spectral function of one-dimensional incommensurate charge density wave (CDW) states and half-filled Mott insulators (MI). The former is characterized by a gap in the spin sector and a gapless charge sector. At $T=0$ there are two dispersing features associated with the spin and charge degrees of freedom respectively. We show that already at very low temperatures (compared to the gap) one of these features gets severely damped. We comment on implications of this result for photoemission experiments. We present a scenario for the evolution from a Mott insulating state to a Fermi liquid as the interchain hopping is increased in a system of weakly coupled chains.