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I use Magento 1.7. The sorting by position dont work in both directions. The url-parameter switch from asc to desc but nothing change in the sorting.
Where could be the problem an in which are the files where Magento sort by position?
As mentioned by roman204 you would need to make sure that the position has been assigned for the product in this category. You can do this via Catalog > Categories:
Required, but never shown