[XeTeX] Computer modern

[Gerrit Sangel]

Hello,

I’m writing an essay with some Chinese Characters in it. This works just fine 
now with Xelatex :D

But because I’m writing it in German, I have to use äöü etc. In normal LaTeX, 
i made \usepackage{lmodern} (it is computer modern, isn’t it? :D) and 
everything worked fine. But if I include this package in Xetex, he gives me 
some errors, so I had to use another font, like Times New Roman. But it is a 
bit ugly imho and it has no ligatures, so I would like to use Computer modern 
again. But if I don’t specify a font the text, he doesn’t display any 
umlauts. 

Is there a way to use a normal LaTeX font? It perfectly suits for me, so I 
would like to continue using it.

And some other question:

What are the commands, apart from \setromanfont, for using another Font for 
the Headlines? If I don’t specify anything, the does not print any 
non-ascii-Character. In German, this may be solved by using another sentence 
where no umlauts are present, but that would not work with Chinese and 
Japanese.

Thanks
Gerrit