RSAKey question

For my CopyProtection-algorithm is use RSAKey. If i encrypt the same data with the same key two times, i will get the same result. So you can draw conclusions that the encrypted data is the same.
Is this the normal behaviour?
So what to do, add some random data to the data?

I certainly hope that encrypting the same data with the same key would give the same result! If you need to hide that fact, then yes, I guess you could just add a couple of random bytes somewhere in your data and it should produce a completely different result.