The court was told that Samantha Kerrigan, 29, from Bonds Hill and Kim Hazlett, 18, from Francis Street were found in a flat with their clothes covered in blood following a row.
They are charged with inflicting grievous bodily harm with intent.
Both women were released on their own bail of Â£500 to appear in court again on 13 August.
They are also charged with false imprisonment and possessing a crutch and brush shaft with intent.
Ms Kerrigan is separately charged with attempting to suffocate, choke or strangle the victim.
Two women have appeared at Londonderry Magistrates Court charged with attacking a man in the city on Sunday.