I have stored some 2-stroke engine stuff for over 20 years with great results. I run the last tank of gas through it with Sta-Bil until the tank is empty and let the gas tank dry out. Then squirt (not pour) a few squirts of oil into the spark plug port and pull the starter a few times. Thats it. Keep it in a dry place and it will last for (well in my case) 20 years. Any good new motor oil will be fine. 2-stroke oil is a little thin, but if its for a year or less storage that stuff is fine. No need to bathe it in oil.
For summer storage around here (during fire season we do not cut much for about 3 months) I just run the last tanks of gas with Sta-bil and run them out of gas and store them. Maybe clean them up at that time too. I do not use oil or solvent or anything. I also keep one or two saws up for general farm work in summer, and for those I use the same pre-mix with Sta-Bil in the gas to keep it fresh for a few months. Seems to work good. I have found that during storage of any kind of engines, gas fouling is the biggest problem in the carbs, usually varnishing them or gumming up the jets.

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So few saws, so many trees...
Stihls: 210/250-/025/290/361/FS85
Echo: CS-3000, Olympyk & Mac doorstops

