Near quenching limit instabilities of concurrent flame spread over thin cellulosic fuel are experimentally studied by employing a narrow channel apparatus. Depending on the oxygen concentration of the imposed flow, two different kinds of instabilities have been identified. Specifically, for oxygen concentration below a critical value, the instability is of fingering or cellular type, whereas for supercritical oxygen concentrations, traveling wave instability prevails, characterized by transverse creeping motion of the flamelets across the fuel edge. Both instabilities are usually accompanied by recurrent flamelet growing and splitting during the flame spread processes. It is justified that the two kinds of instabilities herein identified are diffusive-thermal in nature and may be classified into the category of near quenching limit instability of non-adiabatic diffusion flames. Further, an attempt has been made to gain insight into the physical mechanisms of the flame instabilities by exploiting the similarities between flame spread and smolder wave propagation.