showing ONLY 2nd level menu items (children)

Hello.
After I’ve managed to understand my problem, I now ask a very specific question:
How can I show a menu with only the 2nd level items of the current folder ?
Explanation:
If I’m on a folder page (a page that has children), I want to show only it’s children.
If I’m in a page that has no children - I want it to show nothing.
[Edited - added] If I’m inside a folder, the menu should show any items inside that folder. Example:

If I’m in the "homepage", the second menu would show nothing.
If I’m in the "parent" page, the second menu would show all it’s children.
If I’m in any of the children (child#1, child#2 etc..), the second menu would show all of the children inside the parent page, as described in the line above.
[End of addition]
All the 1st level items, will be in another position in my page and will have no relation with this menu.

Thank you for assisting me in assimilating this wonderful CMS application as my site!

[!DropMenu? &startDoc=`[*id*]` &levelLimit=`1`!]

Thank you Doze for answering.

The problem with the code you gave me, is that it doesn’t show the "friends" of the children.
Explanation:
If I entered a page that has a parent folder, and other items inside that parent folder, I still need to show the other items in the current folder.

I’ve edited the first post to describe it exactly.

use [!DropMenu? &startDoc=`[*parent*]` &levelLimit=`1`!] in the children pages and the above in the folder pages