The delta N formula that relates the. final curvature perturbation on comoving slices to the in. inflaton perturbation on. at slices after horizon crossing is a powerful and intuitive tool for computing the curvature perturbation spectrum from inflation. However, it is customarily assumed further that the conventional slow-roll condition is satisfied, and satisfied by all components, during horizon crossing. In this paper, we develop a new dN formalism for multi-component inflation that can be applied in the most general situations. This allows us to generalize the idea of general slow-roll inflation to the multi-component case, in particular only applying the general slow-roll condition to the relevant component. We compute the power spectrum of the curvature perturbation in multi-component general slow-roll inflation, and find that under quite general conditions it is invertible.