A connector includes a female connector housing, that has a male terminal, and a male connector housing that has a female terminal for electrical connecting to the male terminal, and that is adapted to be fitted into the female connector. The male connector housing includes an inner housing which has the female terminal, and which is adapted to be fitted in the female connector housing so that the female terminal is connected to the male terminal, and an outer housing which is adapted to support the inner housing so that the inner housing is movable in a first direction in which the inner housing is fitted in the female connector housing and in a second direction perpendicular to the first direction. When the inner housing is fitted into the female connector housing, the inner housing is disposed so as to separate from the outer housing in the second direction with a first gap.