Multisolute flow in a nephron model, which includes the Bowman's space, cortical interstitium, and pelvis as well-stirred baths and the postglomerus as a multitube capillary, is investigated. A boundary value problem, which allows for pelvic reflux and consists of a system of differential equations and integral equations, is established. The implicit function theorem is used to establish existence and uniqueness results for the steady-state problem for the case of small permeability coefficients and transport rates.