The gauge is 900 millimetres, a width that is unusual in Germany and is precisely why the street section works - a metre-gauge or standard-gauge train simply could not thread this space. The line runs 15.43 kilometres from Bad Doberan to Kuhlungsborn West, taking about forty minutes end to end, with a maximum permitted speed of 40 km/h that nobody is going to be using in town. Out of the station the train works through the streets, stops at Bad Doberan Goethestrasse as a tram would, then leaves the buildings behind and runs out along an avenue of lindens towards the sea. The transition is abrupt and slightly comic: one moment the locomotive is negotiating a pedestrian crossing, the next it is in open country with a green tunnel of trees closing over it.

On 19 June 1886 Frederick Francis III, Grand Duke of Mecklenburg, granted a licence for a narrow-gauge line from Doberan station to Heiligendamm, and the 6.61-kilometre route opened three weeks later, on 9 July. It was built by a private railway contractor from Stettin, now Szczecin, and worked as a steam tram - later reclassified as a Kleinbahn, a light railway - and at first it ran only in the summer season, from 1 May to 30 September. It existed to carry bathers to the oldest seaside resort on the continent, and it was successful enough that on 13 March 1890 the Grand Duchy nationalised it into the Friedrich-Franz Railway. The decision to push on west came in December 1908, and the extension to Arendsee opened on 12 May 1910. Arendsee merged with Brunshaupten and Fulgen in 1938 to become Kuhlungsborn.

Goods traffic began with the 1910 extension and the trains started running all year. It never really worked. Everything arriving on the standard-gauge Wismar-Rostock line had to be physically transhipped onto narrow-gauge wagons, which was slow and expensive, and the usual dodge - carrying standard-gauge wagons piggyback on narrow-gauge transporter trucks, as the Saxon lines did - was ruled out from the start because of the tight urban section through Bad Doberan. The street that makes the Molli famous is the same street that made it commercially impossible as a freight carrier. Goods services were withdrawn on 31 May 1969. Passengers kept the line alive, and in 1976 the district of Rostock put the railway on its list of protected heritage monuments, which in East Germany was the strongest form of protection available.

Three engines built by the Deutsche Reichsbahn in 1932 - larger, faster and more powerful than anything the line had run before - still do the work today, numbered 99 2321 to 2323. Three more came from the Wismut industrial railways in 1961; of those, 99 2331 survives as the reserve and winter engine, chosen for winter because it is less prone to derailment, while another stands as a monument at Kuhlungsborn West and the third was scrapped. Then in 2009 something almost unheard-of happened: a brand-new steam locomotive, 99 2324, was built for the Molli at the Meiningen steam works, a replica of the 1932 design worked up from historic drawings with modern methods. It was the first steam locomotive built in Germany for regular service in nearly half a century. During trials it ran wearing its sisters' numbers, purely to get the photographers off its back before the official debut.

Demand collapses out of season, so in winter half the trains are cancelled and replaced by the Mollibus, route 121, which runs from Rostock through Bad Doberan and Heiligendamm to Kuhlungsborn and on to Rerik. In 2009 the railway carried 546,415 passengers. Local ownership arrived on 1 October 1995, when Bad Doberan district and the towns of Kuhlungsborn and Bad Doberan took the line over from Deutsche Bahn; the depot and the Molli Museum sit at the Kuhlungsborn West terminus. The line has also acquired an unlikely constituency. Since the 1990s the Molli has been one of the main ways of reaching the Zappanale, the annual Frank Zappa festival held at the racecourse roughly halfway between Bad Doberan and the coast - which means that once a summer, a nineteenth-century Grand Duke's bathing railway fills up with people going to hear Zappa covers.