Youch!  Those 2 things are mega events, which are somewhat random to go off.  There is the option to turn them off when starting a new game, but for your game that's in play already...you will have to tough them out.

Mega Events were made to shake up te game drastically...as you see.

Take some time from attempting to fight them and research bigger hulls, better weapons and better defenses.  Make sure your weapons/defenses compliment their weapons/defenses.  If they got missiles and point defense, go at them with something other than missiles and get yourself some point defense.

Don't attempt to get starbases bakc up and running again until the near-by area is clear.  Probably 2 sectors from the nearest pirate/peacekeeper may be enough to keep them from wandering over and pounding it.

BTW starbase weapons and defenses aren't a challenge to these ships nor mid-end game ships that you can make.  It's just something that doesn't scale that well.

We got to work on your agression issues KP....perhaps have you neutered.  That will also help with the spraying you do...

Yeah yeah...and if we didn't work in packs, the Terrans would have never evolved into family organizations and learned to hunt and then eventually build the hyperdrive that helped all races explode into galactic combat.

See, we really created the hyperdrive, we just lacked the opposable thumbs to assemble/fabricate it.

Back on topic...when mega events happen, roll with the punch and try to turn it into your favor.

Oh yeah...johnlucky, is there an autosave from prior to this happening?  Mega Events are not predestined.  If you could reload to a save game prior to the mega event, you can pick up from there and most likely not be bothered with the pk's nor the mega pirates.

Damn toonces up there got me off track. 

They should all appear at once for 1 mega event.