Alternate Menu for members

You will need two different menus so first we need to register support for two menus in your functions.php file.
Depending on the theme your using you will have some code like the following:

// This theme uses wp_nav_menu() in one location.
	register_nav_menu( 'primary', __( 'Primary Menu' ) );

you will need to add or replace with

register_nav_menu( 'logged-in-menu', __( 'logged-in-menu') );
register_nav_menu( 'logged-out-menu', __( 'logged-out-menu') );

then in your header.php file replace

<?php wp_nav_menu( array( 'theme_location' => 'primary' ) ); ?>

with

<?php
if ( is_user_logged_in() ) {
    wp_nav_menu( array( 'theme_location' => 'logged-in-menu' ) );
} else {
    wp_nav_menu( array( 'theme_location' => 'logged-out-menu' ) );
}
?>

Then in wordpress admin appearance > menus, you should see that under theme locations you have support for two or more menus. Now you can create a menu for logged in users and one for users that are not and apply them to the relevant drop down menus under theme locations.