A fallen tree blocked the Aberdeen-Inverness rail line between Dyce and Inverurie with disruption expected to continue until 6pm.
Earlier, flooding closed the Edinburgh-Aberdeen line in Fife as Storm Francis swept in gales and heavy rain across much of Scotland.
At least nine ScotRail trains were delayed or cancelled by water on the tracks at Burntisland.
Network Rail engineers were checking the site and disruption was expected to continue until 3pm.
In Glasgow, a fallen tree caused a power failure in overhead lines in the east end which was expected to disrupt cross-city services through Queen Street low level station until 4pm.
Network Rail tweeted: “We've located and removed a tree branch that was resting on the overhead lines between High Street and Bellgrove."
CalMac’s west coast ferries were severely affected by the storm, with sailings cancelled on routes such as to Arran, Cumbrae, Gigha, Islay, Kilcreggan, Rum, South Uist and Gourock-Dunoon.
Mattress on M8
On the roads, a tree disrupted traffic on the A82 two miles north of Tyndrum.
A mattress was removed from the M8 west of Glasgow city centre by police and road patrols.
The Tay Road Bridge, along with the Forth Road Bridge – now a bus corridor – were closed to double decker buses.
A fallen tree narrowly avoided hitting a house in Lenzie.
A Met Office yellow severe weather warning for heavy rain remains in force until 6am on Wednesday.
It covers the Central Belt, south of Scotland, Fife and the east coast as far north as Aberdeenshire.
A Met Office spokesperson said: “Storm Francis will bring another spell of very wet and windy weather during Tuesday and early Wednesday.
"Total rainfall accumulations are expected to reach 20-40mm widely with as much as 60-90mm for parts of Northern Ireland and southern and eastern Scotland, particularly over high ground.
"Strong east to north-easterly winds are also expected to develop, with gusts of 50mph affecting exposed coasts and hills.
"The weather will ease from the west from later Tuesday, with eastern Scotland seeing the most persistent rainfall.”
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