I have set a minimum order price but I would like some articles to ignore this minimum.
Where do I start with this?
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Override the method
\Mage_Sales_Model_Quote_Address::validateMinimumAmount and check
$this->getQuote() for the presence of your special articles. I suggest you add an attribute to such articles which are exempt from the minimum order value to easily identify them.
Another approach - without class overwrites would be the following. But I am not sure if it is worth this effort because it does not seem much cleaner: