Mozilla (Firefox 3 or Swiftfox 3) tends to expand its RAM usage according to how much memory is available - it can easily expand to 400 MB or more if I have a lot of windows open. However if I then open several other memory hungry programs (such as GQview in a directory with hundreds of pictures), Mozilla shrinks its RAM usage.

Is there a way of making this happen without deliberately opening other programs?

You have to understand that this is the way Linux was designed. It will use as much of the resources as it needs, until it needs to share those resources. From your description your system is sharing those resources when it needs to. Why would you want to change this?

Unfortunately it uses too much of the resources - when my Mozilla browser is using 450 MB RAM and I'm using 920 MB of my 1 GM RAM, my machine slows down horribly. Changing windows or tabs leads to applications - or sometimes the window manager - hanging for 10, 20 seconds or sometimes even more.

Swiftfox just crashed. Mhen I restarted and all the same pages were loaded, it was using 170 MB, instead of the 480 MB it was using before the crash. (I hadn't restarted off the browser for maybe a week - I prefer to suspend my machine rather than restarting things, especially when I'm traveling and have poor connectivity.)

That sounds more like a bug in your distro (or application not behaving) than a Linux design flaw. The next time you see this slowdown post the results of top and free. This will give us a better idea of what is actually going on.

I thought it was a Firefox design flaw, not a Linux design flaw.

Now I'm using CrunchBang instead of Mandriva, and the same thing happens. It even happens in when I use SwiftFox or SwiftWeasel instead of Firefox, though not as badly.

Will get back to you with the output of top and free.

Firefox I think is well known for hogging memory. That must be due to design choices because Opera certainly uses way less memory lst time I checked. While in essence you should review your whole system for optimal performance (HW, kernel version, scheduler, swappiness and VM sysctls, fs choice, fs mount options) the first thing I'd do to troubleshoot problems with Firefox is create a new clean profile and use that. If that shows way less crashing or memory hogging it may be a Firefox plugin problem.