The extinction of counterflow diffusion flames in counter and co-rotating finite-jets is experimentally and theoretically investigated. In the experimental study of methane and butane diffusion dames, the critical minimum values of oxidizer concentration as a function of the jet angular velocity ω is determined for various values of the jet linear velocity. It is found that the oxidizer concentration at extinction decreases to a minimum value at the critical angular velocity ω = ωr, and thereafter increases with the jet angular velocity. This tendency is similar to that observed earlier for the limiting fuel concentration at extinction. Also, the tests for the extinction of methane flames in counter versus co-rotating jets show that the difference between the results for the two flows appears for ω > ωr,i.e. after the onset of the secondary recirculating flow. Under the latter condition, the limit-oxygen and fuel concentrations are found to be higher in counter versus co-rotating jets. In the theoretical part, the large activation energy asymptotic technique is applied, assuming viscous and incompressible hydrodynamics, for the thermo-diffusive analysis of the diffusion flame structure and extinction with general Lewis numbers of the reactants. Qualitative comparisons are made between the calculations and the laboratory observations. Among possible interactions between stretch rates, vorticity rates and the flamelets, the influence of helicily H = to ω v on the strained diffusion flamelets and its role in the statistical description of turbulent diffusion flames is discussed.