I have a 3 yo filly I'm breaking and have encountered an interesting problem. When she doesn't understand something or just ploain doesn't want to do what I ask, she backs up. Sometimes she gets going really fast and starts pulling her head down like she's going to buck. She's been a great horse to break and I've had very few problems with her. She's the foal of my Mustang mare, so she's smart and in general she's been super easy to work with. She does tend to be bad tempered at times, but I think a lot of that stems from the fact that her mama is the dominant mare in my herd and has spoiled her. I've been asking her to back up as a command, and she does it very nicely and stops when I ask her to. It's just when I don't ask her to that it's a problem. Any ideas?

I would get my legs REAL busy on her until she figures out that backing on her own is not a good idea. Drive her forward every time she does it.

What I'm about to say is completely oppisite from Ranchroper...(no offence Ranchroper)
And I find nothing wrong with his suggestion...just wanted to share some of my own experience.

Metawa did this when I was first training him, and having no one I could ask what to do at that time, and no computer, I decided to try this...

Everytime he backed when he wasn't asked to, I immediately requested him to back..much further and more then he would've on his own...then I praised him for obeying ME, lol.
In other words, I IMMEDIATELY took hold of the situation and made it as if it was MY idea, not his...and I made him work...the last time he pulled it (1997, he had about 15 rides on him) we were out of the pasture and pen, riding around the subdivision...I had asked for a stop and stand...he didn't want to stand and started backing, I turned it into my idea and we backed a half of a country block! LOL! Cured him then and there and he has never done that again. He backs nicely on command, but also knows to stand when asked (or whatever else I'm asking of him)

Good luck

Rearing, backing, and laying down are all refusals to go forward. I will not allow a horse to refuse and duck a cue to go forward. You have to make the desire to go backwards less desirable than the desire to go forward. Going forward is hard for your horse because it is easier to refuse. You have to make the easy thing hard and the hard thing the easier thing to do. Reward the horse for the slightest movement forward and block its attempts to back up, unless you are cueing it to back up.

I have to agree with the guys on this one. I've run into the same problem, and I always treat it the same way. I set up, move the reins in my hand forward up the neck a bit, squeeze with my legs and smootch. When the horse starts backing instead, I continue my position and add rolling my spurs up and down her belly a short distance by just rocking my ankles/toes up and down. As SOON as the horse stops backing I release all pressure and stop all movement. I give it a moment to concider and cogitate, then ask for forward movement again. Any movement forward is rewarded by release from squeezing the legs, any un-asked-for backward movement is rewarded by accelaration and continuation of said discomfort. Set yourself up to succeed in a safe area with good footing and plenty of space when correcting a horse for this.

(and ignore all of my misspelling in above post )

I cured one of my ponies of this by accident. Dixie was a Percheron/Morgan Cross. She was an excellent riding horse except that when she'd get frustrated or tired she'd do just like your mare, duck her head and backup. Dixie did it with a high stomping step. Anyway I was riding her on a dirt road when she got bent about something(?). Anyway she starts backing but the road had a high shoulder that tapered away from the road. Dixie backed into the berm and tripped herself, she fell in slow motion rolling onto her left side. I stepped off and stood beside her. She had come to rest with her feet higher than her body. She tried to gain her legs but couldn't stand. I let her try several times then with me pulling she managed to get up. She was real glad to get back on her feet. Only one more time ever did she start to back without being told. She started and you could see that she remembered her accident. She stopped imediately. I never had the problem again.
I'm not sure you could duplicate Dixie's fall but it danged sure cured her.

Thanks for all the help! I'm fixin' to go out and ride her now. The info. is along the lines of what I was thinking, but this has been a new one - I've just never encountered it before! (Of course, I've only started a limited number of horses, so it's not unusual that I'd encounter something new! )

Just figured I'd give an update on the filly (I haven't had internet for months so that's why I haven't updated before). I worked with her all summer and she turned out to be an AWESOME horse! I sold her a couple of weeks ago , and the girl who bought her says she's doing great. We finally conquered the backing up problem - thanks for the tips!