If a ship has two stress tokens in order to get rid of them I have to perform a green maneuver for two movement phases in a row?

Yep, green moves remove 1 stress each time.

Other abilities and cards can remove stress too.

I thought so, thanks. It's been over a year since I've played but with the impeding arrival of TFA core set I'm getting reacquainted with the rules.

The TFA set has the new Rules Reference Guide, which you can have right now via a PDF from FFG: https://images-cdn.fantasyflightgames.com/filer_public/40/b4/40b44d5f-7a06-406c-ae6e-183c5297e796/swx36_rulesreference.pdf

And all the support files are found here: https://www.fantasyflightgames.com/en/products/x-wing/at the bottom of the page, including the rules guide.

Enjoy!

Thank you.

Well, you don't have to perform the 2 green maneuvers right in a row. You could perform 1 green maneuver to clear 1 stress, then perform white maneuvers for a few rounds, and THEN perform a second green maneuver to clear the second stress. But you have to perform 2 green maneuvers to clear both stress (or have other stress removing upgrades...).