We describe an automatic sequential assignment program (ASAP) for congested solid state NMR (ssNMR) spectra. Given the residue type assignments determined from the well resolved spectra, ASAP first applies auto-residue type assignment strategy (ARTIST) to group individual resonances in unassigned congested spectra into matched residue type assignments, accounting for all possible combinations. Then matched residue type assignment pairs are sequentially allocated by Monta Carlo simulated annealing (MCSA) algorithm. Analytical expressions are derived for critical steps to achieve optimized annealing, in agreement with direct visualization of assignments migration during annealing, provided by the diagnostic tools in ASAP. We point out that there are three types of local minima associated with mis-allocations of assignments in sequential assignment. Owing to the correlation established by ARTIST between inputs, ASAP demonstrates superior robustness against local minima compared to standard MCSA. Alternative strategies are described for accelerated convergence towards global minima and to avoid local minima. Taken together, the efficiency, accuracy and capability of structural determination by ssNMR can be greatly enhanced by ASAP.