[css] CSS: On hover show and hide different div's at the same time?

Here is CSS example how to show hidden div (on hover):

<div class="showhim">HOVER ME<div class="showme">hai</div></div>

and

.showme{ 
display: none;
}
.showhim:hover .showme{
display : block;
}

Can I show one div and hide another one at the same time by using only CSS? Here is example how to use JS for this purpose: http://jsfiddle.net/joshvito/GaZQ6/

Have you tried somethig like this?

.showme{display: none;}
.showhim:hover .showme{display : block;}
.hideme{display:block;}
.showhim:hover .hideme{display:none;}

<div class="showhim">HOVER ME
  <div class="showme">hai</div>
  <div class="hideme">bye</div>
</div>

I dont know any reason why it shouldn't be possible.

if the other div is sibling/child, or any combination of, of the parent yes

    .showme{ _x000D_
        display: none;_x000D_
    }_x000D_
    .showhim:hover .showme{_x000D_
        display : block;_x000D_
    }_x000D_
    .showhim:hover .hideme{_x000D_
        display : none;_x000D_
    }_x000D_
    .showhim:hover ~ .hideme2{ _x000D_
        display:none;_x000D_
    }

    <div class="showhim">_x000D_
        HOVER ME_x000D_
        <div class="showme">hai</div> _x000D_
        <div class="hideme">bye</div>_x000D_
    </div>_x000D_
    <div class="hideme2">bye bye</div>