A theoretical and experimental study of the spin-dependent photoconductivity in dilute nitride GaAsN is presented. The nonlinear transport model we develop here is based on the rate equations for electrons, holes, deep paramagnetic and nonparamagnetic centers under both CW and pulsed optical excitation. Emphasis is given to the effect of the competition between paramagnetic centers and nonparamagnetic centers which allows us to reproduce the measured characteristics of the spin-dependent recombination power dependence. Particular attention is paid to the role of an external magnetic field in Voigt geometry. The photoconductivity exhibits a Hanle-type curve whereas the spin polarization of electrons shows two superimposed Lorentzian curves with different widths, respectively related to the recombination of free and trapped electrons. The model is capable of reproducing qualitatively and quantitatively the most important features of photoluminescence and photocurrent experiments and is helpful in providing insight on the various mechanisms involved in electron spin polarization and filtering in GaAsN semiconductors.