We give lower and upper bounds for the density of the law of a locally elliptic Ito process. Locally elliptic means that the ellipticity assuption holds true only if the process lies in a tube around a deterministc given curve. This represents a generalization of the classical lower and upper bounds for the density of an uniformly elliptic diffusion process but works for diffusions which may be locally degenerated, as the log-normal type diffusion for example. In this case the lower bound is no more Gaussian but has a log normal shape. This also works for Stochastic PDE's.