[en] We investigate the behavior of the zero-temperature quantum non-linear sigma model in d dimensions in the presence of a damping term of the form f(ω) ∼ vertical bar ω vertical bar^α with 1 ≤ α < 2. We find two fixed points: a spin-wave fixed point FP1 showing a dynamic scaling exponent z = 1 and a dissipative fixed point FP2 with z > 1. In the framework of the ε-expansion it is seen that there is a range of values α_* (d) ≤ α ≤ 2, where the point FP1 is stable with respect to FP2, so that the system realizes a z = 1 quantum critical behavior even in the presence of a dissipative term. However, reasonable arguments suggest that in d = 2 this range is very narrow. In the broken symmetry phase we discuss a phenomenological scaling approach, treating damping as a perturbation of the ordered ground state. The relation of these results with the pseudogap effect observed in underdoped layered cuprates is discussed