A zero-dimensional (volume-averaged) and a pseudo-one-dimensional plug-flow (spatially resolved) model are developed to investigate atmospheric-pressure plasma jets operated with He, He/O2, He/N2 and He/N2/O2 mixtures. The models are coupled with the Boltzmann equation under the two-term approximation to self-consistently calculate the electron energy distribution function. An agreement is obtained between the zero-dimensional model calculations and the spatially averaged values of the plug-flow simulation results. The zero-dimensional model calculations are verified against spatially resolved simulation results and validated against a wide variety of measurement data from the literature. The nitric oxide (NO) concentration is thoroughly characterized for a variation of the gas mixture ratio, helium flow rate and absorbed power. An ‘effective’ and a hypothetical larger rate coefficient value for the reactive quenching N 2 ( A 3 Σ , B 3 Π ) + O ( P 3 ) → N O + N ( D 2 ) are used to estimate the role of the species N2(A3Σ, B3Π; v > 0) and multiple higher N2 electronically excited states instead of only N2(A3Σ, B3Π; v = 0) in this quenching. The NO concentration measurements at low power are better and almost identically captured by the simulations using the ‘effective’ and hypothetical values, respectively. Furthermore, the O ( P 3 ) density measurements under the same operation conditions are also better predicted by the simulations adopting these values. It is found that the contribution of the vibrationally excited nitrogen molecules N2(v ⩾ 13) to the net NO formation rate gains more significance at higher power. The vibrational distribution functions (VDFs) of molecular oxygen O2(v < 41) and nitrogen N2(v < 58) are investigated regarding their formation mechanisms and their responses to the variation of operation parameters. It is observed that the N2 VDF shows a stronger response than the O2 VDF. The sensitivity of the simulation results with respect to a variation of the VDF resolutions, wall reaction probabilities and synthetic air impurity levels is presented. The simulated plasma properties are sensitive to the variation, especially for a feed gas mixture containing nitrogen. The plug-flow model is validated against one-dimensional experimental data in the gas flow direction, and it is only used in case an analysis of the spatially resolved plasma properties inside the jet chamber is of interest. The increasing NO spatial concentration in the gas flow direction is saturated at a relatively high power. A stationary O2 VDF is obtained along the direction of the mass flow, while a continuously growing N2 VDF is observed until the jet nozzle.