Multimode combustion (MMC) concepts using homogeneous charge compression ignition (HCCI) gasoline combustion at low loads and spark assisted compression ignition (SACI) gasoline combustion at medium loads have the potential for improved fuel efficiency relative to spark ignition (SI) gasoline combustion. Two MMC concepts are compared in this paper with respect to fuel efficiency and tailpipe NOx emissions. The first concept uses stoichiometric HCCI and SACI to allow standard three-way catalyst (TWC) operation. The second concept also uses HCCI and SACI, but cycles between lean and rich combustion and uses a TWC with increased oxygen storage capacity (OSC) for potentially even greater fuel efficiency improvement. This paper performs a preliminary comparison of the two MMC concepts by analyzing two scenarios: (1) cycling between stoichiometric HCCI at 2 bar BMEP (brake mean effective pressure) and stoichiometric SACI at 3 bar BMEP, and (2) cycling between lean HCCI at 2 bar BMEP and rich SACI at 3 bar BMEP. The effects of excess oxygen ratio during HCCI operation and the frequency of oxygen depletion events on TWC performance and fuel efficiency are investigated. Results show that MMC lean/rich cycling can achieve better fuel efficiency than stoichiometric HCCI/SACI cycling. NOx emissions are moderately higher, but may still be low enough to meet current and future emission regulations.