We consider generalized Forchheimer flows for slightly compressible fluids and study the initial boundary value problem for the degenerate parabolic equation with time dependent boundary condition. We estimate the L∞-norm of the pressure and derive some other estimates. We show that the solutions and its gradient depend continuously on the initial and boundary data and coefficients of the Forchheimer polynomials. De Giorgi and Ladyzhenskaya–Uraltseva iteration techniques are used. Bibliography: 36 titles.