Surface exchange and oxygen vacancy diffusion dynamics were studied in double-perovskites LnBaCo2O5.5+δ (LnBCO) single-crystalline thin films (Ln = Er, Pr; -0.5 < δ < 0.5) by carefully monitoring the resistance changes under a switching flow of oxidizing gas (O2) and reducing gas (H2) in the temperature range of 250 ~ 800°C. A giant resistance change ΔR by three to four orders of magnitude in less than 0.1 s was found with a fast oscillation behavior in the resistance change rates in the ΔR vs. t plots, suggesting that the oxygen vacancy exchange diffusion with oxygen/hydrogen atoms in the LnBCO thin films is taking the layer by layer oxygen-vacancy-exchange mechanism. The first principles density functional theory calculations indicate that hydrogen atoms are present in LnBCO as bound to oxygen forming O-H bonds. This unprecedented oscillation phenomenon provides the first direct experimental evidence of the layer by layer oxygen vacancy exchange diffusion mechanism.