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A new method of hydrogen detection employing a bilayer structure (thin metal-free phthalocyanine and palladium layers) for medium concentration range (1.5% to 4% in air) in the SAW sensor system is proposed. This method is based on the great variation in interaction speeds at various hydrogen concentrations, even though the amplitude signal reaches almost the same frequency level. For a particular chosen initial interaction time interval, a distinct interaction speed can be distinguished with great resolution (from 2.1 Hz/s for 1.5% H2 in air to 21.2 Hz/s for 4%). These initial interaction fragments are linear versus time for the investigated medium hydrogen concentrations in air and nitrogen. In the case of the investigated bilayer structure, the interaction speed is higher in synthetic air than in nitrogen. The difference between these interaction speeds increases at higher hydrogen concentrations.