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This paper shows a numerical evaluation of fuels and additives for HCCI combustion. First, a long list of candidate HCCI fuels is selected. For all the fuels in the list, operating conditions (compression ratio, equivalence ratio and intake temperature) are determined that result in optimum performance under typical operation for a heavy-duty engine. Fuels are also characterized by presenting Log(p)-Log(T) maps for multiple fuels under HCCI conditions. Log(p)-Log(T) maps illustrate important processes during HCCI engine operation, including compression, low temperature heat release and ignition. Log(p)-Log(T) diagrams can be used for visualizing these processes. The paper also includes a ranking of many potential additives. Experiments and analyses have indicated that small amounts (a few parts per million) of secondary fuels (additives) may considerably affect HCCI combustion and may play a significant role in controlling HCCI combustion.