We present measurements of collisional fluorescence quenching cross sections of NO(A(2)Σ(+), v' = 0) by NO(X(2)Π) and O2 between 34 and 109 K using a pulsed converging-diverging nozzle gas expansion, extending the temperature range of previous measurements. The thermally averaged fluorescence quenching cross sections for both species show a monotonic increase as temperature decreases in this temperature range, consistent with earlier observations. These new measurements, however, allow discrimination between predictions obtained by extrapolating fits of previous data using different functional forms that show discrepancies exceeding 120% for NO and 160% for O2 at 34 K. The measured self-quenching cross section is 52.9 Å(2) near 112 K and increases to 64.1 Å(2) at 35 K, whereas the O2 fluorescence quenching cross section is 42.9 Å(2) at 109 K and increases to 58.3 Å(2) at 34 K. Global fits of the quenching cross section temperature dependence show that, when including our current measurements, the low temperature behavior of the quenching cross sections for NO and O2 is better described by a parameterization that accounts for the long-range interactions leading to the collisional deactivation via an inverse power law model.