Did these come in one package ? Something like "X-COM Gold" ? These games are rewritten to make use of directx and windows 95 and there's a known bug with modern videocards (geforce etc.) where pitch is not the same as screen width. The programmers of xcom gold assumed they were the same and the result is a garbled screen like you see now. Someone named f0dder has written a patch which does work for me, you might have to rename the xcom executable if you have a different version but it should work fine, here's an essay about it :
http://f0dder.didjitalyphrozen.com/essay02.htm and more importantly, here's the fix :
http://f0dder.didjitalyphrozen.com/dl/xcom_bugfix05.zip Try it and let me know if it works for you. It works for me even under windows XP.