Even though you believe (or know) that they have not been paying rent, I think it best to treat them like month to month tenants. You need to send them the statutory letter terminating their month to month tenancy. The letter must be sent 15 days before when rent is next due - based on the payment date from the written lease agreement. You could also attempt to simply evict them as hold-over tenants if you are positive that a month-to-month tenancy was not established by any agreement or course of conduct with the prior owner. However, I believe that could still lead to problems for you.
The law is complicated and although the facts expressed may seem to be all that is relevant, there may be many other important facts to consider. Also, the law is constantly undergoing change, so what may be correct today, may not be accurate tomorrow. Only a full consultation with an attorney experienced or knowledgeable in the specific legal subject matter is likely to result in the optimal course of action.
Although the tenants' written lease has expired, it could be that the LL allowed them to stay, paying rent on a month-to-month basis. You will need to review the lease to know if it permits this or automatically converts to a month-to-month lease upon expiration (which is typical). You best, safest, method is to provide the 15-day notice to terminate the lease. If they do not vacate at that time, do not pay rent, or tell you that they are "guests" and not "tenants," then there will be other ways to address the situation. If the tenants refuse to vacate, you should consult with an attorney with LL/T experience and real property law to discuss the full details and your possible strategies.
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