Starting on July 15th, Kazakhstan introduces visa-free travel for 15 days for citizens of United States, the Netherlands, the U.K., France, Germany, Italy, Malaysia, the United Arab Emirates, South Korea, and Japan. It is reported to be a one-year test period to see how it works.
Kazakhstan is one of the 93 countries and territories I have left to visit, but, unfortunately, Denmark is not among the visa-free countries. The Kazakhstan visa is not an easy one to obtain for us other nationalities, but each embassy has different rules. To find more information, I highly recommend the Lonely Planet forum.