Katja -

Without a picture it's hard to tell, but if your spots are small and black, generally appearing on leaf tips first then working down toward the base of the leaf, your collection may have a fungal infection.

To test, cut off a small piece of leaf, place in an airtight baggie, and put in a dark place for a week or so. If the leaf cutting grows lots of mold, then it's a funal infection.

You can purchase a fungicide at your local greenhouse to spray your plants and stop the infection from spreading. Ask first if it is safe to use on orchids. My fungicide is all natural, based on seaweed extract, and has had no noticeable adverse effects on the plant.

Hope this helps!