In this thesis, thermal-diffusive instabilities are studied experimentally in diffusion flames. The novel species injector of a recently developed research burner, consisting of an array of hypodermic needles, which allows to produce quasi one-dimensional unstrained diffusion flames has been improved. It is used in a new symmetric design with fuel and oxidizer injected through needle arrays which allows to independently choose both the magnitude and direction of the bulk flow through the flame. A simplified theoretical model for the flame position, the temperature and the species concentration profiles with variable bulk flow is presented which accounts for the transport properties of both reactants. The model results are compared to experiments with a CO2-diluted H2-O2 flame using variable bulk flow and inert mixture composition. The mixture composition throughout the burning chamber is monitored by mass spectrometry. An elaborate calibration procedure has been implemented to account for the variation of the mass spectrometer sensitivity as a function of the mixture composition. The calibrated results allow the effective mixture strength of the diffusion flames to be measured with a relative uncertainty of about 5 %. In order to properly characterize the flame produced, the velocity and temperature distribution inside the burning chamber are measured. The resulting species concentration and temperature profiles are compared to the simplified theory and demonstrate that the new burner configuration produces a good approximation of the 1-D chambered diffusion flame, which has been used extensively for the stability analysis of diffusion flames. The velocity profiles are also used to quantify the residual stretch experienced by the flame which is extremely low, below 0.15 s-1. Hence, this new research burner opens up new possibilities for the experimental validation of theoretical models developed in the idealized unstrained 1-D chambered flame configuration. The thermal-diffusive instabilities observed close to extinction are investigated experimentally and mapped as a function of the Lewis numbers of the reactants. The use of a mixture of two inerts (helium and CO2) allows for the effect of a wide range of Lewis numbers to be studied. A cellular flame structure is observed in hydrogen flames when the Lewis numbers is relatively low with a typical cell size between 7 and 15 mm. The cell size is found to scale linearly with the diffusion length, in good agreement with theoretical predictions. When the Lewis number is increased by using a higher helium content in the dilution mixture, the instabilities observed are planar intensity pulsation. The use of methane allowed pulsating flames to be generated for a wide range of bulk velocities and transport properties. The pulsating frequencies measured are in the 0.7 to 11 Hz range and were found to scale linearly with a diffusion frequency defined as U2/Dth multiplied by the square root of the Damköhler number. The experimental results presented here are the first observations of thermal-diffusive instabilities in such a low-strain flame. They constitute a unique dataset that can be used to quantitatively validate theoretical models on diffusion flame stability developed in the simplified one-dimensional configuration.