* E.ON, RWE, EnBW nuclear tax bill so far 5 bln euros

* EU court says is compatible with EU law

* German constitutional court decision to come (Recasts, adds comments from E.ON, EnBW, updates shares)

LUXEMBOURG/FRANKFURT, June 4 (Reuters) - A German tax on the use of nuclear energy does not breach European Union laws, Europe’s top court said on Thursday, dealing a blow to utilities’ hopes for a multi-billion euro refund.

Germany’s top three energy groups - E.ON, RWE and EnBW - have said the tax, of which they have paid about 5 billion euros ($5.67 billion) - is illegal and favours other electricity sources, demanding the tax be repaid.

“By today’s judgment, the Court of Justice replies that EU law does not preclude a duty such as the German duty on nuclear fuel,” judges at the Luxembourg-based Court of Justice of the European Union (ECJ) said.

The court also said the Germany duty on nuclear fuel did not constitute illegal state aid.

The decision is another blow to the country’s utilities, already suffering from a decision to shut down all nuclear power plants by 2022, as well as a surge in rival renewable energy as part of Chancellor Angela Merkel’s policy of “Energiewende”.

At 0931 GMT, E.ON shares were down 1.4 percent, while RWE’s fell 2.1 percent. Thinly-traded EnBW shares rose 1.3 percent.

Germany’s utilities are now pinning their hopes on a related lawsuit filed with the Constitutional Court, the country’s highest legal body, which theoretically could still rule the tax illegal.

“This is not the end of it, since today’s decision only referred to the question whether the tax is in line with European law. Germany’s Constitutional Court is examining the tax’s conformity with German law in a parallel case,” a spokesman for E.ON said.

A decision is expected in the course of the year, and one in favour of the utilities could still pave the way for the tax to be refunded, a spokeswoman for smaller peer EnBW said.

The judgment came four months after an ECJ adviser backed the German tax in a case brought by German company Kernkraftwerke Lippe-Ems, which operates the Emsland nuclear power plant in Lingen, in the northwest of the country.

So far, E.ON has paid 2.3 billion euros in nuclear fuel taxes, while EnBW has paid 1.1 billion. RWE will have paid 1.6 billion euros by the end of the year.

The levy requires firms to pay 145 euros per gramme of nuclear fuel each time they change a fuel rod, usually about twice a year.

The duty is designed to cover some of the cost of storing radioactive waste based on the polluter pays principle.