Is there a statute of limitations for a guarantor?

No. There is no statute of limitations "for a guarantor". However, there are statutes of limitations for different categories of debts. Statutes of limitation vary from jurisdiction to jurisdiction and for different types of contracts. For example a five year lease, a thirty year mortgage, a six year car loan. However, in the case of a default by the primary borrower, a creditor will generally seek payment from the guarantor prior to the tolling of the statute of limitations.