- QCD3 is a superrenormalizable massless theory; therefore off-mass-shell infrared divergences appear in the loop expansion. We show how certain infrared divergences can be subtracted by changing the boundary conditions in the functional integral, letting the vector potentials approach non-zero constant values at infinity. Infrared divergences, in the Green's functions, come together with powers of logarithms of the external momenta, and among the infrared divergences we deal with, there are those that give rise to the leading and first subleading logarithms. We show how for two-point functions it is possible to sum the leading and first subleading logarithms to all orders. This procedure defines a nonperturbative approximation for QCD3. We find that in the ultraviolet region these summations are well defined, while in the infrared region, some additional prescription is needed to make sense out of them. From the construction developed to cancel infrared divergences, we derive the presence of arbitrarily large field strengths in the vacuum. We respect Lorentz invariance, because in this construction, one averages all directions and strengths of these fields. Possible applications to the infrared problem of QCD4 are indicated.