The sliding arc discharge starts at the shortest distance between the electrodes, then moves with the gas flow at a velocity about 10 m/s and the length l of the arc column increases together with the voltage. When the length of the gliding arc exceeds its critical value lcrit, heat losses from the plasma column begins to exceed the energy supplied by the source, and it is not possible to sustain the plasma in a state of thermodynamic equilibrium. As a result, a fast transition into a non-equilibrium phase occurs. The discharge plasma cools rapidly to a gas temperature of about T0 = 1000 K and the plasma conductivity is maintained by a high value of the electron temperature Te = 1 eV (about 11,000 K). After this fast transition, the gliding arc continues its evolution, but under non-equilibrium conditions (Te = >> T0). Gliding discharges comprising both equilibrium and non-equilibrium plasma conditions offer high energy efficiency and selectivity for chemical processes. Prevailing parameters satisfying non-equilibrium plasma conditions at relatively high power levels should be well understood and characterized. In the present work, gliding discharges formed between diverging electrodes in air flow are discussed. These were studied experimentally over a wide range of gas velocities and power levels. Depending on the system parameters the following discharge regimes were observed: low power non-equilibrium discharge; thermal quasi-equilibrium discharge; and gliding discharge with equilibrium to non-equilibrium transition. The effect of system parameters on discharge characteristics is analyzed. The equilibrium to non-equilibrium transition was experimentally observed as a change of voltage increase rate with discharge length growth. The local electric field, defined as dV/dl, increased up to three times, indicating the change of plasma conditions. However, previously reported phenomenon of length explosion was not supported by our experimental data. The co-existence of equilibrium and non-equilibrium phases is also discussed in the frame of phenomenological theory, assuming formation of a growing non-equilibrium fragment inside the gliding discharge channel. It was found that high flow velocities provide intensive cooling, an increase of electric field, and a decrease of gas temperature, promoting equilibrium to non-equilibrium transition at high power levels.