The Brief: Ze, zir, and zem are variations of gender-neutral third person pronouns.
Ze, Zir, Zem, Zeir
Ze – pronounced “zee” –and its variations: zir, zem, and zeir, are gender-neutral pronouns that can be used to refer to people who are non-binary, genderfluid, genderqueer, trans, and/or don’t identify with the gender binary. Other variations and tenses of these pronouns include zyrself and zirself. Ze pronouns are often used alongside hir pronouns, with different uses for different tenses and forms, usually “ze, hir, hirs, hirself.”
More Gender-Neutral Pronouns
Ze/zir/zem/zeir are one set of gender-neutral pronouns. Other commonly used gender-neutral pronouns include they/them/their, Xe/Xir/Xem/Xeir, and hir/hirself. Trans people sometimes use binary or non-binary pronouns, depending on what their gender is and how they identify.
The best way to avoid using the wrong pronouns to refer to someone is to ask them which ones they use and to let them know which ones you use.