  We analyze the time variability of the X-ray emission of RE J1034+396 -- an
active galactic nucleus with the first firm detection of a quasi-periodic
oscillations (QPO). Based on the results of a wavelet analysis, we find a drift
in the QPO central frequency. The change in the QPO frequency correlates with
the change in the X-ray flux with a short time delay. The data specifically
suggest a linear dependence between the QPO period and the flux, and this gives
important constraints on the QPO models. In particular, it excludes explanation
in terms of the orbiting hot spot model close to a black hole. Linear
structures such as shocks, spiral waves, or very distant flares are favored.
