As long as they are like tires, i.e. radials you should be technically OK IMHO. That being said the tires are designed to be used in sets. Many people on this forum mix and match tires, they get better wear or grip out of a certain tire, or they feel the handling is better with certain mixed tires. The bike may handle differently depending on how the bike goes into a turn, for example; the front may fall in easier then the rear, thus not working in concert with each other.
Another issue you may want to think about is when you do need the new tire, the old one is now... well, old. Again handling maybe sacrificed.
Tire purists and tire manufactures may tell you never mix them. Others will say it doesn't really matter.
I personally like my tires to match; however, in a pinch, I have had mixed tires even on the FeeJ. I bought it with Avon's then I needed to replace the rear they only had a B021. Then I stuck on a front Dunlop Roadsmart, then I finally got a set PR2's.
Good luck.