We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full nonlinear equations that relate the primordial perturbation to the curvaton perturbations on large scales, calculate the power spectrum of the primordial perturbation, and finally go to second order to find the nonlinearity parameter, fNL. We find large positive values of fNL if the energy densities of the curvatons are subdominant when they decay, as in the single curvaton case. But we also find a large fNL even if the curvatons dominate the total energy density in the case when the inhomogeneous radiation produced by the first curvaton decay is diluted by the decay of a second nearly homogeneous curvaton. The minimum value min(fNL)=-5/4 which we find is the same as in the single-curvaton case.