If both files belong to the same clientlib, you can affect their order in the resulting CSS by modifying the css.txt
file. It should be just next to the CSS files themselves and it lists them all by relative path.
If the CSS files come from different client libraries, you can try introducing a dependency between the clientlibs, as explained here.
However, the fact that the order is relevant may be a sign that your CSS selectors are not specific enough. If I were you, I'd try improving the CSS itself before modifying the order in which the files are loaded. Using specific CSS classes for different elements of your page would give you a lot more control over the design.