NOVELTY - The hydrogen generator (1) comprises a de-sulfurizer (4), a modifier having a modification catalyst which generates a hydrogen-containing gas from the raw material, a combustor (5) for heating the modifier, an ignition device, and a controller (8). The hydrogen generator starts combustion of the combustor using the de-sulfurized raw material during start operation. The controller lengthens the ignition operating time of the ignition device during start operation according to the failure of pressure of gas flow path or de-sulfurizer during stop period.    USE - Hydrogen generator is used in fuel-cell systems (claimed) for generating hydrogen-containing gas as fuel. The fuel-cell systems are used as electric-power generating apparatus of distribution-type energy supply source, and for cogeneration systems.    ADVANTAGE - The hydrogen generator prevents the possibility of combustion state in a combustor turning into a quasistable state by ignition miss.    DETAILED DESCRIPTION - The hydrogen generator (1) comprises a de-sulfurizer (4) which contains a de-sulfurizing agent which absorbs-and-removes sulfur compound in the raw material, a modifier having a modification catalyst which generates a hydrogen-containing gas from the de-sulfurized raw material, a combustor (5) for heating the modifier, an ignition device for igniting with the combustor, and a controller (8). The hydrogen generator starts combustion of the combustor using the de-sulfurized raw material during start operation. The controller lengthens the ignition operating time of the ignition device during start operation according to the failure of pressure of gas flow path or de-sulfurizer during stop period. INDEPENDENT CLAIMS are included for the following:    (1) operating method of hydrogen generator; and    (2) operating method of fuel-cell system.    DESCRIPTION OF DRAWING(S) - The drawing shows the block diagram of the fuel-cell system.    Hydrogen generator (1)    De-sulfurizer (4)    Combustor (5)    Fuel cell (7)    Controller (8)