Which is the right There "seem" / "seems" to be?

This is a subject-verb agreement issue: Because this is an inverted sentence, with the subject coming after the verb, we can become confused. Rephrased in its natural order, it reads, "Two main causes of long-distance relationships seem to be the following (there)." We can now more easily see that the subject is "causes" (plural) requiring the plural form of the verb "seem" (without an "s"). So the answer is "There seem to be two main causes..."

Depending on noun here the correct option is

There seem to be two main causes of long-distance relationships.

If the sentence had singular noun, "seem" would be used.

There seems to be one cause of long-distance relationships.