The 60-day notice law, Civil Code, Sec. 1946, is triggered when property is rented for "a term not specified by the parties". If the parties agreed to a fixed term, with no provision for automatic renewal or the lease becoming month-to-month at the end of the agreed term, then that law does not apply and the agreed end-date governs.

If there is a provision for automatic renewal or month-to-month extension, the parties rights may be affected by those terms of the lease. For example, even if the lease has a fixed term, if it does not require advance notice of intent to automatically renew, a landlord's silent expectation that the tenant will simply move out may be met with a surprise, late renewal of the lease by the tenant. If the lease automatically becomes a month-to-month lease, the tenant may have an argument for at least one additional month's tenancy if notice is delivered within the last month of tenancy. These are theoretical examples, not certainties -- it is important to review the actual lease.