Patriarchal behavior, such as other social habits, has been transferred online, appearing as misogynistic and sexist comments, posts or tweets. This online hate speech against women has serious consequences in real life, and recently, various legal cases have arisen against social platforms that scarcely block the spread of hate messages towards individuals. In this difficult context, this paper presents an approach that is able to detect the two sides of patriarchal behavior, misogyny and sexism, analyzing three collections of English tweets, and obtaining promising results.