A connecting structure has a male terminal (10) including a tab (13) and a female terminal (20) including a rectangular connecting tube (23) that receives the tab (13). A louver spring (30) is housed in the connecting tube (23) and has two spaced apart contact piece rows (31) each including juxtaposed resilient contact pieces (35) with contact portions (36) facing each other. The tab (13) resiliently contacts the contact portions (36) by being inserted between the contact portions (36) while resiliently displacing the contact piece rows (31) at the opposite sides. Inclined surfaces (15, 16) are formed adjacent a tip of the tab (13) of the male terminal (10) to gradually thin the tab (13) toward the tip. The inclined surfaces (15, 16) are formed so that the positions of base end edges (15A, 16A) connected to flat surfaces 14A differ in forward and backward directions.