The reason that I asked which cars you have is because LGB has three different groups of cars that could be considered to be part of an "alpine series".
The smallest represent the Zillertal Bahn. This is a narrow gauge railroad in the Austrian alps. These cars are short and have two axles. The LGB Zillertal cars are about 10 inches long. My Zillertal coaches are in Arizona so I couldn't take a picture of them for comparison, they are similar in size to the car in the top of the picture.
In the 1980s LGB came out with a series of Swiss (RhB) 4 axle passenger cars. These are intermediate in size. This car LGB #3064 and it is about 18 inches long.
In the 1990s they came out with the longest Swiss (RhB) cars. The car on the bottom is LGB #30650 and it is 25.5 inches long. My guess is that this is similar to the ones that are giving you trouble. While LGB designed these to be run on all radius curves, R1 (4ft diameter), R2 (5 ft diameter), and R3, they are best run on R3 (8ft diameter) or larger. I even had trouble with mine derailing on Aristcraft 10 diameter curves. As others have said check that the track is level (across the track). Does it derail when you run the train in the opposite direction. I have found that sometimes running counterclock wise rather than clock wise will solve the problem.
You still haven't said what diameter you are using and how many cars you are pulling. Try starting out with one car and see how it runs, if it doesen't derail, then keep adding a car until you have a problem. This is the kind of information that we need to be able to help you.
Chuck