The influence of nitrogen cluster states (CS) on the conduction band (CB) structure of GaAs1-xNx is probed by measuring the effective mass and gyromagnetic factor of carriers for a wide range of nitrogen concentrations (from x < 0.01% to x = 0.7%). An unusual compositional dependence of these two important CB parameters is found. This behaviour is well reproduced by a modified k·p model taking into account the nonmonotonic loss of Γ character of the CB minimum due to multiple crossings between the red-shifting conduction band edge and N cluster states. Analogously, sudden variations in the exciton mass can be externally induced by applying a hydrostatic pressure, which brings the upward moving CB edge into interaction with N states which at ambient pressure are resonant with the GaAs1-xNx CB continuum.