In a structure of fitting female and male connectors together, the female connector includes a female housing, and a female adapter which is provided on the female housing, and has a guide groove, and is fitted on a fitting portion provided at the male connector. The male connector includes a guide rib which is formed at the fitting portion, and is engageable in the guide groove. The female adapter can be rotated relative to the female housing to be placed at any of a plurality predetermined angular positions arranged with a fixed interval, and can be attached to the female housing. Only when the female adapter is rotated into a preselected one of the plurality predetermined angular positions, and is attached to the female housing of the female connector, the guide rib can be fitted in the guide groove, thereby allowing the female and male connectors to be fitted together.