In this paper, sufficient conditions for the existence of a solution to the non-linear H-infinity filtering problem are presented. The conditions are expressed in terms of the solution to a Hamilton-Jacobi inequality involving only n + 1 (for time-varying case) or n (for time-invariant case) independent variables. Both affine and general non-linear systems are examined. In the time-invariant affine non-linear case, one kind of positive radial solution to the Hamilton-Jacobi inequality is presented, and an explicit estimation of the achievable disturbance attenuation level is given. Illustrative examples are also included.