Will be making a connection in LAX on American and will have to go between Terminal 3 and 4. How easy is this? Do you go "outside", i.e. outside security then back thru security or do they have a "passover"?

Terminals 3 and 4 are across from each opther. Separated by parking areas. You can see what they look like from here:
http://www.quickaid.com/airports/lax/

thanks nice website.
Can you get from Terminal 3 to 4 without going outside of and then back into security?

It doesn't seem so. You gotta go out of the building to get to terminal 4. Bummer.....

It doesn't seem so. You gotta go out of the building to get to terminal 4. Bummer..... The web site also says there is an airport shuttle system to take passengers between terminals. This lead one to believe that they are separated.

John:
The free shuttle service is located on the lower level. Runs avery few minutes.
We have walked from Terminal 2 to the International Terminal in less than ten minutes.
John

Thanks John. It's not the walk but the secrity issue that is of concern, i.e. time consuming waits. Or is LAX more resasonable than Logan?

You will go thru security again when you change terminals. Security once when you board your flight to LAX, and again when you board your flight from LAX. Make sure your connections are not too tight.

All in all LAX is a pretty user friendly airport. You will need to go back through security but they have their acts together a bit better than what I've been hearing about Logan. You can check your bags straight through and the shuttle is easy to take. Lower level stand under the appropriate sign for the "A" shuttle. You could walk it by cutting through the parking lots, but I wouldn't risk getting lost if you don't know the airport. The International Terminal (Tom Bradley) is between terminal 3 and 4.