Another view of it.

Yes it looks like some kind of fungus. Just part of the decomposition process, harmless to the plant, which is still alive, or to people. Sounds/looks like it likes the moist space between the inner pot and cache pot. When you water, make sure the plant is finished dripping before putting it back in the cache pot. If it's really grossing you out, you could remove the old soil and replace with new. If there's enough space without causing the inner pot to sit too high, a few small rocks (not a layer of tiny pebbles) at the bottom of the cache pot, as long as they stay dry, could allow enough air flow for this to stop being noticeable.

Thank you!
As it isn't harmful, I will likely just leave it alone, other than being more careful when watering and raising the pot a bit.

Yeah, it's just breaking down the organic stuff in the pot. Knowing that, you can also know the pot will hold water for increasingly longer periods as the particles become smaller and more closely lodged together (which also means the tiny air pockets can disappear.) If the plant grows fast enough, that can be mitigated by simply having more roots using more water. Can you tell what the soil is? Looks like just peat but I suspect there's some bark or other organic particles. Not that familiar with peat and the fungi that might get on it, but that looks like a fungus one would see in a mulched bed outside. Looks like a slime mold, or dog vomit fungus. Great names that are helpfully descriptive. Anyway, when you repot, you'll probably find a mini quasi-representation of natural soil layers in there, with all of the smallest particles having shifted to the lowest part of the pot.

I don't know how fast these plants grow, just got one recently myself. (This forum is dangerous for enabling!) But know that the rate of water use could slow down because of the decomposing action in the pot if the plant doesn't grow pretty fast. Hopefully someone who knows this plant better can jump in here with some more specific advice. I'm going to repot mine soon because the pot is so small, it's not able to stay upright. It's so full of roots, I can't see anything but a little peat at the surface.

If your plants' pot has just pure peat, its' chances for survival are not as high. I know what happens when peat and I (and my watering can) get together. My plants end up dead from root rot. It always looks dry to me, so I water. The peat holds so much moisture, and its' tiny particles lodge so closely together, filling all spaces where tiny air particles should be, that watering as often as I think I need to causes the roots to rot. People come here constantly with ill plants from this very thing.

So this brings us back to the soil thing. I think this discussion has some great info about that, if you're interested in investigating. Learning about how a more porous, chunky, airy soil can be so helpful to plants is what has helped me stop killing plants. There are many ways to accomplish this, many 'ingredients' or ways of doctoring store-bought. Most people find something that's so much more pleasing than plain peat, or just bagged potting soil. I stopped using peat a long time ago, very positive results, but didn't really understand this particle-size thing, or drainage in general until much more recently. This added info, along with the premise that all plants are growing from the roots up, has decreased the mortality rate of plants at my house to almost zero. There's always room for improvement!

I wish the pics were a little more close up, but I think you should look carefully at the white yuck and see if it isn't soil mealybugs.

Here is a link that might be useful: a thread about fungus and soil mealies.

Hmm...
I think the safest thing might be to repot. It is in a bit of REALLY fluffy peat because I haven't done anything at all to it other than sit it down, water once, and recently pick it up to notice the... stuff.
This plant is pretty well segregated from all others in the house (at least 7 feet from its nearest neighbour), so maybe spreading won't be a problem.
I'm not sure if it is just fungus or what aseedisapromise has pointed out in the other thread. Maybe thoroughly washing the roots will help it go away.
I'll report back.

Ewww! In the other thread, it says they don't move. (That's not fair play by the bug world, BTW, like scale.) It seems really important to make sure it's not that, and follow advice if so. TY, Aseed! Babbling about decomposition and roots may not be relevant at the immediate moment.

It's a harmless mold (fungus). Not slime 'mold ' and not soil mealies. Same stuff has been submitted to the forums countless times.

Well great! I've never heard of soil mealies, that I remember, and it's not been a pleasant learning experience here today, though for the best I'm sure. Back to the original impression of the fuzzy pics seen through bifocals... harmless decomposition that I didn't know was so strict about its' common names, though it all is the same to me, 'mulch rot' if another common name won't cause too much ruckus. They sometimes do, though, oh brother.

Hey, for me, these were fairly crisp, in-focus pictures! ;-)

I decided that I would repot. I removed from the pot & used the hose to clean as much soil as I could. Then I rinsed the pot well. And then I used white vinegar on it (the pot), then rinsed again, and set it aside.

The roots actually looked decent to me. If it was harmless mould, surely the repotting won't hurt. Especially as I got it out of the super-fluffy peat!

I will note that there were distinct striations of soil.

This post was edited by ariel7576 on Fri, Aug 23, 13 at 0:20

There was this roughly triangular thing on the caudex-like base. Any clue?

I just wanted the OP to look closely, and to think about isolating his/her plant from the rest of his/her collection. I think the questioner should have all the possibilities before him/her. I am happy he/she is repotting. I am not sure about the triangular thing, is it loosely attached, or on tightly/part of the caudex? If no one else says anything I would put the question in a new post about it with a link back to this thread. You could also ask on the cactus/succulent forum.

He/I is/am keeping the pony tail palm fairly well isolated from other plants. I'm going to keep an eye on things.
The repotting can only help, given the soil it was in before. I haven't gone to a true Al's Gritty Mix, but the new soil is pretty chunky, so that can't hurt.

The triangular thing is attached fairly tightly to the caudex. It seems to be part of it. At first, I thought it was wax. I might be able to scrape it off, but I'll wait until it is time to either repot or to deal with any reoccurrence of the original mould/mealies/whatever.

I'm pretty sure I got the plant on clearance, so I'm okay taking an observational stance for now.

Thanks for all of the suggestions and responses from everyone.

"Hey, for me, these were fairly crisp, in-focus pictures!" Sorry, it's probably time for new bifocals!

"taking an observational stance" Prudent, I like this.

Sending good vibes!

purple, I'm a bit notorious for taking blurry pictures! I'm lucky if part of my hand isn't showing up in the iphone pictures.
I'll update on the PT's progress, if any progress there be.

VERY off-topic: I went to law school in New Orleans, so your username ALWAYS seems like "purple in OPP" (Orleans Parish Prison) to me! ;-)