Native responding - at last.

The perception of this sentence would differ with its context.
By itself, the statement sounds odd because of the definite article.

If the statement came in the middle of a conversation discussing two different social systems, and everyone knew which two were being referenced, then the sentence is perfect as it is.

However, in isolation, the reader doesn't know which two social systems are being referred to, so at first glance it seems to imply that there are only two social systems in existence in all the universe. THE two social systems. There are no others.

This native speaker's first reaction to that sentence, outside of any context, is to remove the "the" and make it a global statement about two unspecified social systems, which allows for the fact that others also exist.

I hope that didn't confuse you. %}

So I guess the sentence should be:

We believe that peaceful coexistance of different social systems is fully possible.

Right?

"We believe that peaceful coexistence of two different social systems is fully possible."
(If the number two is in some way germane.)
Or your version, al_ex_an_der, if the number is not relevant.

In any case, "coexistance" needs to be changed to "coexistence".

Thank you! I corrected the eror in the word.
Existas only two social systems: the Capitalist and the Socialist. They are discussed here. So "the" is appropriate here, isn't it?

If those two systems are discussed immediately before this sentence, then yes, "the" is appropriate.

Yes. Thank you.

Removed @change tag and added OK.