The necessary conditions in the microscopic derivation of the Ginzburg-Landau (GL) equations are discussed, by showing that for a Pippard-or an intermediate-type superconductor the GL equations are valid only in a rather narrow region. Basing on the Gorkov equations for the thermodynamic Green functions of superconductor and using a nonlocal series of the "Green function of normal metal" in the magnetic field, we have derived a pair of coupled integro-differential equations for the energy-gap function and vector potential. These equations are valid for the Pippard- and intermediate-type superconductors in the same region near Tc as that for the London-type. The equations are applied to a semi-infinite superconductor in a static magnetic field. The integral expressions for energy-gap function and penetration depth are given. In the London and Pippard limit the integrals are performed analytically. For a superconductor of the Pippard-type, the corrections of energy-gap function and penetration depth due to magnetic field are calculated in the whole region near Tc. It is shown that the behaviour of a Pippard-type superconductor differs much from that predicted by the GL theory.