Processes are disclosed for the preparation of 2-methylfuran and 2-methyltetrahydrofuran. The continuous vapor-phase processes are commercially viable and efficient because they permit the preparation of 2-methylfuran and 2-methyltetrahydrofuran using commercially-available catalysts, namely, a reduced copper-based catalyst consisting essentially of cupric oxide, chromium (III) oxide, manganese oxide and barium chromate and a reduced nickel-based catalyst consisting essentially of nickel, nickel (II) oxide, aluminum oxide and silica. An apparatus comprising two inline hydrogenators is used for preparing the 2-methylfuran or 2-methyltetrahydrofuran.