I tried changing the behaviors of pop-up, when second one has to appear at first. The text is appearing fine but then the text gone for first one.

Hey @Sonja 

Thank you so much for reaching out to the Klaviyo Community for help! We love that you are making your site more accessible to customers with different language signup forms! How to customize content based on language has some incredible resources to help users to reach more of their customers in their own languages, including signup forms like you created!

Since it seems like you were able to successfully publish the forms to your site, the problem with certain text not appearing may be due to conflicting Javascripts. With the experience you are having, it seems similar to this previous Community post from @dhbien.itprog :

There may be Javascript on your site that is conflicting with the signup forms you created on Klaviyo. This conflict could prevent the Klaviyo code from working properly. I would recommend reaching out to a developer if you're unfamiliar with Javascript processes or reaching out to members of our extensive network of agency partners for help identifying any conflicting Javascript on your site. 

I hope this helps get you and your site back on track quickly!! Thank you for being a member of the Klaviyo Community!