The present work aims to study the quenching of propagating flames in meso-combustors for which dimensions are of the order of quenching distances of hydrocarbon fuels. Combustion of gaseous fuels and subsequent flame propagation in a meso-scale combustor duct of square cross-section is studied experimentally. Premixed mixtures of methane, propane, and ethylene with air are considered. Two different variants of flame propagation states are found to occur in the meso-combustor, viz., one undergoing flame propagation till the combustor entry and quenching at the step and the other undergoing wall quenching. Regime transitions across these flame states are mapped comprehensively over a wide range of operating conditions. The radius of curvature of the flame and the dead space between the flame and the wall are determined for those conditions with the aid of curve fitting and image processing techniques using Matlab software. The spatial and temporal variation of both these parameters show a drastic increase during quenching in the wall-quenched case, while it remains nearly constant in the step quenched case. With increasing duct Reynolds number, the flame propagates slower, and the heat conduction to the wall leads to a decrease in the dead space and flattening of the flame, particularly at equivalence ratios corresponding to lower flame speeds. This flame-wall interaction is found to be low for methane, resulting in more heat loss and thereby wall-quenched flames compared to propane and ethylene. None of the ethylene flames were found to suffer wall quenching thereby making it a suitable fuel for meso-/micro-combustors among the three fuels used in the present work.