I was using the -d flag, but it wasn't enough.  I was able to get two cgminer instances running by using the "--remove-disabled" option (as found here: https://bitcointalk.org/index.php?topic=227230.0).  It tells the cgminer instance to completely ignore the other GPUs on the system.  

Script 1:

export DISPLAY=:0
export GPU_USE_SYNC_OBJECTS=1
export GPU_MAX_ALLOC_PERCENT=100
./cgminer -o tcp+stratum://pooledbits.com:8338 -u <user> -p x --scrypt --api-listen --api-network -I 18 --auto-fan --gpu-powertune 20 --gpu-engine 960 --gpu-memclock 1220 --gpu-platform 0 -d 0 --remove-disabled -w 256 -v 1 -g 1 -l 1 --thread-concurrency 8000

Script 2:

export DISPLAY=:0
export GPU_USE_SYNC_OBJECTS=1
export GPU_MAX_ALLOC_PERCENT=100
./cgminer -o tcp+stratum://pooledbits.com:8338 -u <user> -p x --scrypt --api-listen --api-network -I 20 --auto-fan --gpu-powertune 20 --gpu-engine 900 --gpu-memclock 1250 --gpu-platform 0 -d 0 --remove-disabled -w 256 -v 1 -g 1 -l 1 --thread-concurrency 21712

However, I'm still having the HW errors on my 7770.  It's using the options specified in Script 1, and it having lots of HW errors.  After running for 10 minutes, I had almost 900 errors.  My video card is an MSI R7770-PMD1G5d: http://www.msi.com/product/vga/R7770-PMD1GD5.html
It's supposed to be able to run at 1 GHz and has "4500" MHz Memory (I don't actually believe that, so I set it to 1220).  

Long time reader - first time poster

I am using cgminer 3.3.0 on Ubuntu 12.04 to mine litecoin.  I have two different video cards: 7950 and 7770.  I expect to be getting about 660Kh/s and 170Kh/s respectively.  

When I configure my command line options and specify to use one card, I get expected results.  When I try to combine those options into one command, the 7770 card is only doing about 16Kh/s.  Apparently you can't run two separate processes with different options - I was getting hardly any hashes when I tried to do that.  

Here's my command:

./cgminer -o tcp+stratum://pooledbits.com:8338 -u <user> -p x --scrypt --api-listen --api-network -I 18,13 --auto-fan --gpu-powertune 20 --gpu-engine 925,1000 --gpu-memclock 1250,1125 --gpu-platform 0 -w 256 -v 1 -g 1 -l 1 --thread-concurrency 21712,8000

The other part that I can't figure out is why I get HW errors on the 7770 if the Intensity is above 13.  As far as I can tell, I've followed all the suggestions for options, and specified everything for each card exactly as it should be.  

Any help is appreciated!