In the first place, you cannot require more than 20 day's notice of your tenants. Here, it was kind and sensible of you to give them 60 days advance notice, but the City of Seattle has very specific rules about how you terminate a tenancy in Seattle. If you google "Just Cause Seattle tenancy termination" you will find the rule.
Assuming arguendo that your notice is valid, it can be effective July 31. This is because you can't contract around the RLTA. See RCW 59 18 230. Having given them notice, they are under no obligation to give you notice back. I hope this helps. Elizabeth Powell
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Your tenants are welcome to give their own notice to vacate and move earlier. For a notice to be effective, it must be given at least 20 days before the end of the month for a date that is the last day of the month. RCW 59.18.200. If your tenants move without notice, they are liable for all rent that would accrue for the 30 days following the date they move, i.e. for the next month's rent. RCW 59.18.310.
What can you do? You can sue them for non-payment of rent when the rent falls due if they don't pay. If they're still there, you can give them a three day notice and potentially evict them. If they've moved, you can sue for the money (and any damages) in small claims court for up to $5,000.00 or in another court if there are more damages. You could also hire a collection agent to do it for you.