But the idea is gradually taking hold: the Japanese, Koreans and Americans are all developing their own versions; and German techno-optimists think they are ready to go.
If the Transrapid line is built, it will carry passengers by rail from Berlin to Hamburg in 55 minutes. At present, the train journey takes about four hours; Europe's fastest trains could do it in two; and the plane takes an hour. The floating train, in other words, is in a different league.
On its test track, the Transrapid can reach speeds of more than 300mph. Its supporters - including the German Ministry of Research and Technology, eager to have something to show for the pounds 700m of taxpayers' money that has already been spent - say that a brave new world of travel is just around the corner.
The basic idea is not new. Hermann Kemper, a German engineer, first took out a patent in 1934 for a 'levitation system with wheel-less vehicles, levitated by means of magnetic fields along iron guideways'.
Kemper's ideas are closely reflected in the magnetic levitation, or 'Maglev', train being developed today. It is supported by electromagnets, attached like claws along both sides of the bottom of the train. The contraption hovers just above its tracks, thus completely avoiding wheel friction: it is supported, propelled and braked contact-free.
Theoretically, the attractions of the Transrapid, and similar hover-trains, are many. At 200mph, it is said to be quieter than a car at 70mph. It copes with climbing better than a conventional train, which would mean fewer expensive tunnels. Its energy consumption is less than that of existing trains, let alone aircraft. Several ideas for proposed routes were abandoned before the former transport minister, Gunther Krause (who resigned in a corruption scandal, earlier this year) argued that the Transrapid should run from Berlin to Hamburg. The Finance Minister, Theo Waigel, has until now been cautious. He has emphasised that private industry should dip into its own pocket more deeply if the government is to participate in building the line, at an estimated cost of pounds 4bn. Private investors have just come up with another 'final' offer and the government could give its provisional blessing as early as this week, with construction starting in 1997.
German railways and the German airline, Lufthansa, would theoretically be involved once Transrapid is up and running, though their enthusiasm is muted. Lufthansa would lose much of its domestic business to Transrapid, and German Railways, due to be denationalised next month, makes it clear that its first love is still the ICE, the high-speed train introduced two years ago.
Transrapid's advocates argue that if the South Koreans or Japanese put passengers quickly inside their Maglev trains, they could dominate the market, if the technology takes hold. In Japan, a stretch of Maglev track is already being built.
Chancellor Helmut Kohl may be blamed, whichever way the decision goes.
If the government now says yes to Transrapid, he will be accused of squandering billions of marks if it all goes wrong. If he says no, he will be blamed for lack of vision if Maglev trains prove to be the transport of tomorrow.