Hi MaTam,
“Probably one option is displayed in the desktop version, the other in the mobile version” – I think you are correct. It will be your theme that is outputting the menu twice, so you would need to edit your themes template files (usually the header.php file) to remove one of the calls to wp_nav_menu. You may then need to adjust the theme CSS to make sure the desktop menu also appears on mobile.
Regards,
Tom