In previous work, we discussed the detection of reverberation delays in the narrow-line Seyfert 1 (NLS1) 1H0707−495. The delays originate close to the black hole. Here, we show that RE J1034+396 shows very similar lag properties. At low frequencies (<1 × 10−4 Hz), the time lag between energy bands increases with energy separation, similar to that commonly seen in Galactic black holes and other active galactic nucleus. At higher frequencies (∼3.5 × 10−4 Hz), the soft (<1 keV) and hard (>3 keV) bands lag behind the intermediate band (1–3 keV). The simplest interpretation is that the intermediate band is dominated by the direct power-law continuum, while the soft and hard bands are dominated by the relativistically smeared reflected emission. The low-frequency delays are present in both available observations. The high-frequency lags are only seen in one observation. In the observation where high-frequency reverberation delays are observed, the spectrum contains a power-law component and there is a quasi-periodic oscillation (QPO) in the light curve. In the other observation, no power-law component is required and no QPO is seen. The lags originate a few gravitational radii from the black hole, and the QPO is associated with the power-law-emitting corona.