He can give you two notices. The 60 day notice terminates the month to month tenancy. The 3-day notice to pay or quit only comes into play if you do not timely pay. If you pay he has to wait the 60 days. If you do not pay he can file when 3 days have past.
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I'm aware of no statute that explicitly states that a landlord can give you 60 (or 30) days notice for a no cause eviction at the same time as he delivers notice for late or nonpayment of rent. That said, there's also no statute that explicitly prohibits it.
There is a statute (ORS 90.401) that expressly authorizes landlords to simultaneously pursue multiple actions causes of action, but it clearly identifies a number of implicated statutes and the no-fault eviction procedures (ORS 90.427) aren't amongst them.
In practice, landlords do this all the time to ensure that if you do ultimately pay your rent they can nonetheless rely on the no-fault notice when the deadline arrives. Despite the timing, there is almost no attorney that would advise you to pursue challenging a no-fault notice absent other actions on the part of the landlord that would otherwise give rise to a habitability, retaliation, or other such significant claim.
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I agree with the other attorneys about the 60 day notice. Regarding the 72-hour notice, I have a couple of things to add:
With the past notices, if the landlord accepts rent for three rental periods after the notice, then that notice is considered waived. However, this wouldn't affect the most recent 72-hour notice.
Also, if there's a signed rental agreement that says when rent must be paid, it doesn't matter when you told him you would pay. If there's no such agreement, and you have always paid your rent on the third Wednesday, then that is the day when rent is due. Under ORS 90.394(2)(a), the landlord can give you 72-hour notice "no sooner than on the eighth day of the rental period, including the first day the rent is due." The 3rd Wednesday this month is the 18th, so he shouldn't be able to serve the notice until the 25th. However, if you wish to fight the 72-hour notice, you need to: (1) be sure there never was a written agreement (or that the agreement allowed for 3rd Wednesday payments), (2) consistently have paid on the 3rd Wednesday (and be able to prove it), and (3) pay January rent on time. Of course, if we're talking about December and he just now gave you the 72-hour notice, this argument goes right out the window.
Under ORS 90.394(3), a 72-hour notice must also "specify the amount of rent that must be paid and the date and time by which the tenant must pay the rent to cure the nonpayment of rent." This means, it must give you the opportunity to pay the rent within a certain amount of time to avoid termination. ORS 392 describes a tenant's right to "cure" a violation. Under ORS 392(4)(a), the period for curing the non-payment of rent, must be either: (A) 14 days from receiving the notice, or (B) "If the violation is conduct that was a separate and distinct act or omission and is not ongoing, no earlier than the date of delivery of the notice as provided in ORS 90.155. For purposes of this paragraph, conduct is ongoing if the conduct is constant or persistent or has been sufficiently repetitive over time that a reasonable person would consider the conduct to be ongoing."
Since you have received those ten other 72-hour notices, you are likely to run into some problems with "curing the violation." Under ORS 392(5)(a), If the cause of a written notice delivered under subsection (1) of this section is substantially the same act or omission that constituted a prior violation for which notice was given under this section within the previous six months, the designated termination date stated in the notice must be not less than 10 days after delivery of the notice and no earlier than the designated termination date stated in the previously given notice. The tenant does not have a right to cure this subsequent violation." I still think you can make several arguments here:
(1) Your landlord waived most of the old 72-hour notices by accepting rent;
(2) The past payments were all really on time (IF you met the requirements I laid out above);
(3) The most recent 72-hour notice actually has to state the no right to cure language;
(4) The fact that ORS 392(5)(b) says, "A landlord may not terminate a rental agreement under this subsection if the only violation is a failure to pay the current month’s rent."
It sounds like you might have some arguments against the 72-hour notice. I think the 60 day notice is going to be a problem for you unless you can prove he's retaliating against you for doing something you have a right to do (you need to read the things listed under ORS 90.385), or there's some sort of written lease term that he's breaking and the contract doesn't allow for 30/60 days notice. Overall, from your post, it seems like there may not be much of an argument against the 60 day notice.
If you want to read more about any of the statutes I've referred to in this post, here's the link: http://www.leg.state.or.us/ors/090.html
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