there are browser specific CSS bits that only work in specific browsers.
There are also bits of the standard that aren't implemented in all browsers.
IE8 doesn't implement all of CSS3, neither do old versions of Chrome and Firefox.
So either work around the problem by not using things that aren't supported in the browser versions you're targeting or change the browser versions you target to include only those that support what you're using.
Just to add... What styles are you applying that are not working? There could possibly be some work arounds (alternative approach, vendor specific properties, etc..) but you haven't provided much info so providing additional guidance is challenging.