Divorce courts in the United States can hear cases only if they have jurisdiction over the parties. You may file for divorce in a state if you are a resident, but you can pursue the divorce only if you give legally sufficient notice to your spouse of the action. Both state and international law can be relevant to the kind of notice required if your spouse is in Mexico.
Service of Process
When you want to sue somebody, you must give her notice of the lawsuit; this is called serving process. State law specifies what kind of process is required in a divorce case. Generally, an adult other than yourself hands a copy of the initial court papers to your spouse. You may proceed with the divorce whether she responds or not.
Personal Service in Mexico
If your state law permits personal service of a person abroad, you can serve a spouse in Mexico with process by having an adult go to where she is and hand her a copy of the papers. Note that this service, while legal in the United States, will not be accepted in Mexico.
Serving Process in Mexico
If you wish to enforce your divorce judgment in Mexico, you must use a means of international service that is accepted by that country, usually Letters Rogatory. These methods are more complex than personal service. The requirements are described in the Inter-American Service Convention and the Hague Convention on the Service Abroad of Judicial and Extra Judicial Documents.