The Homogeneous Charge Compression Ignition (HCCI) concept shows great potential for improving engine efficiency and reducing pollutant emissions. However, the operation with this concept in Internal Combustion (IC) engines is still limited to low speed and load conditions, as excessive Pressure Rise Rates (PRR) are generated with its fast auto-ignition. To overcome this limitation, the use of moderate thermal and charge stratification has been promoted. This leads to multi-stage ignition, and thus a potentially acceptable PRR. Recently Sarathy et al. (2019), three-stage auto-ignition has been emphasized as a chemical phenomenon where the thermal runaway is inhibited during the main ignition event. The current paper demonstrates experimental evidence on this phenomenon observed during n-heptane and n-hexane auto-ignition at lean diluted conditions in a flat piston Rapid Compression Machine (RCM). Multi-stage ignition events caused by either chemical kinetics or by the well-known thermal stratification of this type of RCM are clearly identified and differentiated. The combination of these two factors seems to be a suitable solution to overcome PRR limitations.