Peacekeepers

It is a random event.

I have played 100s of games and never had it.

If you have a save game from the turn before the event, you can always reload the turn.  I do that with the Jagged Knife event because it is simply too annoying.  (It guarantees a win, but it is t e d i o u s)

On Peacekeepers, I have seen others post that you simply research and wait.  Eventually, you will be strong enough and, in the meanwhile, no other AI can do anything either.  For example, if you go up in engine tech and miniaturization, you can launch a ship or two and lead them around the galaxy and then you build/launch other ships to do what you want. 

The Peacekeeper event is an annoying random Mega event, but its not beyond fixing. If I recall correctly, they are like pirates; they can't produce new ships and their ships tend to remain in the sector they are found in. You should be able to clear out a sector, then build up an army of ships safely in that cleared out sector, then clear out adjacent sectors, and so on. Hopefully at some point, you will have your empire cleared of Peacekeepers while your enemies don't, giving you an advantage when you start attacking them.

You should also research techs to improve your ships to better kill them since they are likely to have powerful high quality ships (relative to the strongest civs) and lots of them.

A mega-event not so fixable is the 5 parsec per turn event (may come with different speed limits). You can't fix that, and the max speed for any ship is 5 parsecs. Its quite crippling on larger maps, such as immense maps with its 22 sectors by 22 sectors (it would take over 100 turns to get from one end of the map to the other other with this event).

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If you are new to this game, I suggest you consider turning off Mega-events when you can choose pregame settings. We (the experienced players) asked for harder games and so we got Mega-events as one of the new features. It might be too much for a new player.

Thanks for all your helpful replies.

I must be unlucky as its happened twice to be in 2 games!

wait till you get the dread lords as one of the starting races!

There's always been a theory that some "random" mega events are not entirely random but influenced by how you've played the game so far.
E.g. the peacekeepers would more often show up if the game has been quite focused on aggression

Not sure if it's really the case but it could very well be and that would also explain why people that stick to 1 gameplay style see some events far more often than others.

That is definitely the case. I haven't yet figured out any of the exact triggers, but at least in case of the 5pc/week Speed Limit event, I'm certain it is only happening if your ships fly above a certain speed. I haven't seen this event since I began to only use a maximum of one or two engines per ship, except once. In that game, the Ultradrive random event (+50% to speed) occurred, increasing the speed of some ships to 13 or 14, not sure exactly. Shortly after, the Speed Limit event occurred.

I've discovered in the past that if you play the game with cheats enabled and use Ctrl-Y to trigger a mega event, the events differ from game to game. So while the actual occurrence of any given mega event may be random, there are definitely some kind of conditions that need to be met for them to happen.

I've read about this before^ you can add a ship to every fleet with warp bubble III on it which will raise the fleet speed to +8 per turn.Not much I grant you but you'll still be faster than your enemies.