Tenant won't move after 30 days notice ( month to month)

[Ann Wu]

Hi all, I have a tenant that he is possibly not moving after 30 days of notice.  The date is not there yet but I am pretty sure he won't move. He has been paying the rent on time. But since it's month to month lease now, I would like to replace the tenant. The tenant now is acting really strange.  So, I wonder if he is not willing to move, what should I do? I live in Texas and can not find any UD eviction ways. Thanks for answer in advance.