The theory of excess carrier transport with zero magnetic field in a nondegenerate semiconductor with position-dependent energy gap is presented. It is assumed that the change of energy gap is moderate at the distance of the Debye length and in consequence the quasi-neutrality principle is fulfilled. As the basis the transport equations of the thermodynamics of irreversible processes are chosen. Formulae for the total current density J and for the effective field J /σ are derived. It is shown that in addition to the ohmic component the expression for J /σ contains the Dember effect, bulk photovoltage (Tauc's effect) and f µ component, the last of these being connected with the position dependence of mobility which is rather unavoidable in the case of a variable energy gap. The continuity equation is formulated as an extension of Roosbroeck's continuity equation for a homogeneous semiconductor. Most typical applications of one-dimensional equations in an approximate form are examined, which is important from the practical point of view.