Improving mixing between two coaxial swirled jets is a subject of interest for the development of next generations of fuel injectors. This is particularly crucial for hydrogen injectors, where the separate introduction of fuel and oxidizer is preferred to mitigate the risk of flashback. Raman scattering is used to measure the mean compositions and to examine how mixing between fuel and air streams evolves along the axial direction in the near-field of the injector outlet. The parameters kept constant include the swirl level $$S_e = 0.67$$ S e = 0.67 in the annular channel, the injector dimensions, and the composition of the oxidizer stream, which is air. Experiments are carried out in cold flow conditions for different compositions of the central stream, including hydrogen and methane but also helium and argon. Three dimensionless mixing parameters are identified, the velocity ratio $$u_e/u_i$$ u e / u i between the external stream and internal stream, the density ratio $$\rho _e/\rho _i$$ ρ e / ρ i between the two fluids, and the inner swirl level $$S_i$$ S i in the central channel. Adding swirl to the central jet significantly enhances mixing between the two streams very close to the injector outlet. Mixing also increases with higher velocity ratios $$u_e/u_i$$ u e / u i , independently of the inner swirl. Additionally, higher density ratios $$\rho _e/\rho _i$$ ρ e / ρ i enhance mixing between the two streams only in the case without swirl conferred to the central flow. A model is proposed for coaxial swirled jets, yielding a dimensionless mixing progress parameter that only depends on the velocity ratio $$u_e/u_i$$ u e / u i and geometrical features of the swirling flow that can be determined by examining the structure of the velocity field. Comparing the model with experiments, it is shown to perform effectively across the entire range of velocity ratios $$0.6 \le u_e/u_i \le 3.8$$ 0.6 ≤ u e / u i ≤ 3.8 , density ratios $$0.7 \le \rho _e/\rho _i \le 14.4$$ 0.7 ≤ ρ e / ρ i ≤ 14.4 , and inner swirl levels $$0.0 \le S_i \le 0.9$$ 0.0 ≤ S i ≤ 0.9 . This law may be used to facilitate the design of coaxial swirled injectors.