Menus don't switch according to languages

Your theme probably suffers a very frequent bug.
Please go in the theme code and look for the instruction register_nav_menu and wp_nav_menu and report their parameters here.

Thank you for quick reply. Here is the excerpt from header.php :

<?php do_action('et_header_menu'); ?>

					<nav id="main-menu">
						<?php
							$menuClass = 'nav';
							if ( get_option('trim_disable_toptier') == 'on' ) $menuClass .= ' et_disable_top_tier';
							$primaryNav = '';
							if (function_exists('wp_nav_menu')) {
								$primaryNav = wp_nav_menu( array( 'theme_location' => 'primary-menu', 'container' => '', 'fallback_cb' => '', 'menu_class' => $menuClass, 'echo' => false ) );
							}
							if ($primaryNav == '') { ?>
								<ul class="<?php echo esc_attr( $menuClass ); ?>">
									<?php if (get_option('trim_home_link') == 'on') { ?>
										<li <?php if (is_home()) echo('class="current_page_item"') ?>><a href="<?php echo esc_url( home_url( '/' ) ); ?>"><?php esc_html_e('Home','Trim') ?></a></li>
									<?php }; ?>

									<?php show_page_menu($menuClass,false,false); ?>
									<?php show_categories_menu($menuClass,false); ?>
								</ul>
							<?php }
							else echo($primaryNav);
						?>
					</nav>

and from functions.php:

function register_main_menus() {
	register_nav_menus(
		array(
			'primary-menu' => __( 'Primary Menu', 'Trim' )
		)
	);
}
if (function_exists('register_nav_menus')) add_action( 'init', 'register_main_menus' );

Your code looks good ??

I went back to your site and it seems that the problem is now fixed. Am I right?

Not quite, unfortunately. If you switch to Russian, the menu does switch to the Russian version, too. But it doesn’t remain a Russian one if you proceed to another menu item, it switches back to English.
The goal is to have a Russian menu active as long as I move around in Russian section of the page.
What could be a cause of this behaviour and how to fix it?

Oh I see. The problem is that you did not create menu item with Russian pages but with English pages. You must change your menu items in your Russian menu and slect Russian pages.

You must change your menu items in your Russian menu and slect Russian pages.
And how do I go about it, precisely, I’m a bit confused as to where to change this?

Now, I got it, thank you so very much. Your help is very appreciated.

You must change your menu items in your Russian menu and slect Russian pages.
And how do I go about it, precisely, I’m a bit confused as to where to change this?
This still stands true, the changes I made didn’t work. So how can I fix this issue?

In Appearance->menus, you have to create one menu per language. Let’s say ‘menu_en’ and ‘menu_ru’.
In ‘menu_en’, you add English pages and the language switcher. In ‘menu_ru’, you add Russian pages and the language switcher.
Then, once menus are both saved, you click on ‘manage locations’ tab and you assign ‘menu_en’ to ‘Primary menu English’ and ‘menu_ru’ to ‘Primary menu Русский’.

Thank you so much. It works just fine.