We study transport properties of thin films near the superconductor-in
sulator transition. Formulated in a phase representation, the key new
feature of our model is the assumption of a local Ohmic dissipative me
chanism. Coarse graining leads to a Ginzburg-Landau description, with
non-Ohmic dynamics for the order parameter. For strong enough damping
a new universality class is found. It is characterized by a nonunivers
al de conductivity, and a damping-dependent dynamical critical exponen
t. The formulation also provides a description of the magnetic-field-t
uned transition. Several microscopic mechanisms are proposed as the or
igin of the dissipation.