1. Lieutenant Governor Assumption: Upon the Governor's resignation, the Lieutenant Governor immediately becomes the new Governor of New Mexico. The Lieutenant Governor serves the remaining term of the former Governor.
2. Special Election: If the vacancy occurs more than 18 months before the next regularly scheduled general election for Governor, the Lieutenant Governor holds office as the acting Governor. However, a special election is held to fill the remainder of the term. The special election takes place on a date set by the Governor, with a maximum interval of six months from the date of the vacancy.
3. Appointment by the Legislature: If the vacancy occurs within 18 months of the next general election, the Legislature fills the vacancy. Within 30 days after the vacancy, the Legislature meets in special session and elects a new Governor from among its own members. The elected Governor serves the remainder of the term.
4. Temporary Appointment by the Governor: If the Legislature is not in session at the time of the vacancy and cannot be immediately convened, the Governor may appoint a temporary successor. This temporary appointment lasts until the Legislature can convene and elect a new Governor as described in point 3.