Do the cars derail if run around the 18" curves each separately? If not, then add one car, and try them. I'll bet the corner of the cars are touching on the inside of the curves. If that is the case, you will need to use longer coupler shanks to get more spacing between the cars. If there are diaphragms on the ends, they could be rubbing. You may need to shorten them. That will leave a gap when on the straight track, but it can't be helped. Also, with the couplers, you may need to not only use ones with longer shanks (Kaydee sells some), but modify the pockets to permit wider swing of the coupler. If you can't conveniently do that, you might want to try using a drawbar between the cars. That will mean you can't uncouple them, but chances are you will run them altogether anyway.
You may also need to check the swing of the trucks. It is possible that the sideframes will need to be modified, especially on the truck ends. As a final possibility, you may need to cut clearances in the skirts where the trucks hit them.
Because my father and I used to ride the same type of cars on the C&NW from Chicago to the suburbs, I bought two of the Kato cars myself (in C&NW livery). While I was able to work these on 18" radius, with modifications described (except for NOT having to cut away the side skirts), I found it the better part of valor to increase the radius of curvature on my new layout (in progress after 20 years hiatus). But I didn't have room to use 22-inch curves, so I compromised by using Shinohara 20-in. radius, rather than Atlas 18 or 22-in. Most folks don't realize the availability of other than Atlas 18 and 22" curved snap track, but Shinohara has a whole bunch of different curves up to and including 30-inch! You can get them from Walthers. They aren't cheap, but they'll do the job for you.
Green board, Pard!
My suspicion was the steep grade up to a bridge, so I removed it, but still no better. They most frequently de-rail along my 18'' radius curves, and so I believe it has to do with the trucks not having enough side-to-side motion. What should I do? 
(Also, they are the same length as some Santa Fe cars I have, and those work flawlessly).
