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There's noting wrong with asking the tenant to move.....and if the tenant is a month-to-month tenant, then they're only entitled to 30 days at a time. If you've issued a notice to the tenant to move and they refuse, the only other option you have is to sue and evict the tenant. This process varies depending on your state.......if you'll let me know what state you're in, I'll try to find a guide for this.
No, it's not really an issue IF the tenant only holds a month-to-month lease. In that case, you can give notice and if the tenant doesn't leave, you can sue for eviction.
Here's a good link that outlines the tenancy termination process for Arizona: http://www.nolo.com/legal-encyclopedia/arizona-notice-requirements-terminate-month-month-tenancy.html
Basically, you just have to issue a 30 day written notice to vacate......and if the tenant isn't out after the 30 days expire, you can go to your local small claims court and file an eviction action.
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