Time-series measurements of OH concentration have been obtained in turbulent counterflow nonpremixed H-2/CH4/air flames to study the influence of turbulence parameters on the dynamics of such flames by independently varying the Reynolds number (Re) and global strain rate (SR). The autocorrelation functions from the measured time series are found to be self-similar and can be fully characterized by their integral time scales. The integral time scale displays a power law dependence on both Re and SR. At lower strain rates, fluctuations in the OH layer are nearly independent of Reynolds number. An increase in SR changes the spatial displacement of OH, paving the way for faster fluctuations of the OH layer at higher Reynolds numbers. Both the bulk strain rate and Reynolds number scale linearly with the jet exit velocity (U). Furthermore, the combined effect of SR and Re on the integral time scale behaves approximately as U-1.35 in these counterflow nonpremixed flames. Hence, the Re-1.4 dependency previously observed for the OH integral time scale in jet diffusion flames is likely due to a combined effect of jet exit velocity on both strain rate and Reynolds number.