The results on the measurement of electrical conductivity and magnetoconductivity of a GaAs double quantum well between 0.5 and 1.1 K are reported. The zero magnetic-field conductivity is well described from the point of view of contributions made by both the weak localization and electron-electron interaction. At low field and low temperature, the magnetoconductivity is dominated by the weak localization effect only. Using the weak localization method, we have determined the electron dephasing times and tunneling times t . Concerning tunneling, we concluded that t presents a minimum around the balance point; concerning dephasing, we observed an anomalous dependence on temperature and conductivity ͑or elastic mean free path͒ of . This anomalous behavior cannot be explained in terms of the prevailing concepts for the electron-electron interaction in high-mobility two-dimensional electron systems.