Yes, you can evict a tenant without a written lease in Florida, but you must follow the legal process, which requires written notice and a court order. For nonpayment of rent, a 3-day notice to pay or vacate is required; for other issues or no specific cause, a 15-day notice is typically required to terminate a month-to-month tenancy.
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The information for this answer was found on our Florida Eviction Process answers.