They look a lot like Bulbophyllums in the section Megaclinium. Don't know the species. These all come from Africa. Yes, not all Bulbos come from tropical and subtropical Asia and the South Pacific Islands, there're also a few in South America (Bulb ipanemense).
Here's Bulbophyllum (Megaclinium) purpureorachis:
http://www.orchidoman.net/bulbopurpureorachisplant.jpg
Another species is Bulbophyllum (Megaclinium) falcata:
http://kojimatsk.hp.infoseek.co.jp/g...um20010304.JPG
They're pretty cool and pretty weird.
Yours also looks like it's been over exposed to the sun. Try growing a bit shadier and give them enough water to stay evenly moist (which means watering everyday, preferably with the best water you can provide), and see if they'll turn green.
Whatever you do,
DO NOT REMOVE THE ORCHID FROM THE "STUMP", whatever the "stump" is. I'm assuming that "stump" is some sort of weird and unusual African plant that goes dormant or something. If that "stump" is alive, you gotta find out what it really is. Unfortunately, I'm not a native African plant expert, I'm just an orchid/bromeliad dork. If you're in Cape Town, there are lots of botanists in your are. Some specialize in Disas. For example there's Hildegard Crous. She's well reknown where you live.
You could ask someone from the Kirstenbosch National Botanical Garden what that stump is. Send them a picture when it has leaves. Also give them a picture without leaves.
If that "stump" is dead.
AGAIN DON'T REMOVE THE ORCHID FROM THE "STUMP". Leave it alone, that'll be your mount from now on, and it looks cool anyways.
Good luck.