In the first, police say a woman of 23 was gang-raped and murdered last week in Rohtak district - it took days for her mutilated body to be found. A post mortem showed her "skull was broken".
On Saturday a 22-year-old was gang-raped in a moving car in the Delhi suburb of Gurgaon, police say.
Activists say both attacks show women continue to be unsafe in India.
Residents in Sonipat district, where the Rohtak victim's family lives, found the woman's decomposing body after they noticed stray dogs around it.