The first one is a "hammer" coral and is not looking to well, the second one is possibly a "torch" coral. Both belong to the same family group I believe. For identification links, please see my Coral page.
Thanks Chuck for the ID help. I have come across your site before and I must say that you have a wealth of information about corals.
I also envy the fact that you're somewhere near rich fishing and reef areas of the Philippines. I was born and raised in Manila but have been here in the USA for all of my adult life. I miss the days when I went out with friends to collect livestock to stock our aquariums with.
I better stop blabbering cause I can go on and on. Do you think there's hope for these corals? The damage was caused by transport. I did my best to clean the corals our before placing them in my tank. I hope that with good care and water quality they survive the ordeal. They've been in the tank for about 4 days now and have been opening up beautifully (despite the damage). I have one more ID request if you don't mind.
The first two are both Euphyllia sp. Off the top of my head the first looks like an ancora, or hammer coral. The second is possibly a torch or frogspawn. If you have very clean water and provide these corals moderate light and moderate current (not too much) they have a good chance of surviving. Good luck!
On your picture P8293848.jpg I looked it up in Julian Sprung's "Corals A Quick Reference Guide" and on page 134 it shows a purple version of what your picture shows. So it might be a Cynarina - Meat, Knob or Doughnut coral.
It looks similar to C. lacymalis - the one I want! LOL
Update: The first two corals (hammer and torch(?)) are doing real well. They're opening up and taking in a lot of light. The 3rd coral, Cynarina, is not doing too well. It has not opened up at all and looks like a goner. I'm still hoping for it to recover.