Yes, you can evict a tenant without a written lease in California, 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 quit is required; for other issues or no specific cause, a 30-day notice is typically required to terminate the tenancy (or 60 days if the tenant has lived there for one year or more).
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The information for this answer was found on our California Eviction Process answers.