I am in the Duchal Palace, but the darn Greater Doppelgangers are so fast! They can kill me before I get to the second round of attack! So any strategy for killing them?

Doppelgangers can have their haste dispelled. Also, summons will aid in occupying at least some of them, so make sure you have charged wands available. Web (can be a blessing or a curse) is a consideration, especially if your melee fighters have some form of immunity (Freedom spell, rings etc.)

To compound on Hickory's statement, Slow also helps with those Doppelgangers, as well as the entangle spell iirc.

1) Summoned Creatures.
2) Haste on your party members.
3) And/or the potion for fighters that works like haste, coupled with the one augmenting their HP and fighter prowess.
4) Greater malison followed by Hold person, and/or web.
5) If you can afford it, a heal or two on the key, vital grand dukes.

A very hard place. Dukes die, you 're dead. Best strategy is to kill the things quickly. Blocking their movements with many summons, always works well. In the originals twice so, because summons end up conjuring LARGE numbers of creatures at once!

If you have access to this spell at the time, Otiluke’s Resilient Sphere is a good way to ensure the grand dukes survive this harsh encounter.
And as said earlier, Dispel Magic is a must have to get rid of these dopplegängers under amphetamines (might be one of the most useful spells of BG1). Just be sure it is the first spell you launch if you don’t want to dispel your Otiluke’s Resilient Spheres ;)

Potions, which were mentioned in the post above, are a great bet.

At this stage of the game you'll probably have a lot of cash left over (if you did enough side-quests) and there won't be much left to spend it on. Also, if you're the type to hoard stuff, you may have stacks of potions sitting in some character's inventory. If not, mage stores like Sorcerous Sundries (the big one near the city gate) sell them. This is the endgame, so it's the ideal time to start using these things.

In Baldur's Gate, healing potions are very weak, but buffing potions are extremely strong. They last a long time (5-10 minutes real time, typically. Sometimes much longer.) and have very powerful effects. There are potions that give you 50% magic resistance, potions that improve your armour class to the level of full plate even if you're wearing leather, potions that make you immune to certain damage types, potions of giant strength that can give your characters up to +6 to hit and + 12 damage, depending on how much strength they had to start with...

It's not a subtle or a clever solution, but drinking down a gallon of these things will make almost any fight you're struggling with into a very manageable dust-up.

Edit: just be careful combining this strategy with the dispelling one mentioned above, since you can and will dispel your own potion effects. Dispel Magic is also the factor that made me write "almost" in the "almost any fight" sentence I wrote above.

Okay... now I'm the mazes of jelly! UGH!

Two words: deadly traps!

Be happy, is not a tomb of horros with spheres of the anhilation inside of the statute mouth :P