I want to buy a trademark, that has been cancelled in 2006. Can I just apply to buy it or do I notify the previous owne
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In the U.S., trademarks exist, or not, without regard to the status of a registration. So, even if the federal registration has been cancelled, as I infer from your question it has been, if the owner of the mark is still using it, you would need to acquire the mark and the good will from the current owner. If you did so, you could thereafter file a new federal trademark registration application in your own name--you cannot transfer or buy a "cancelled trademark." If no one is using the mark, it may well be available for you to begin using it without having to buy it from the current owner.