The Met Office has issued yellow warnings of heavy rain in Aberdeen, Aberdeenshire, Angus, and Perth and Kinross, which is in force until 11am on Thursday, while a warning for Moray and the Inverness area expires at 8am.
The Scottish Fire and Rescue Service said it was called to reports of flooding in Ellon, Aberdeenshire, from around 4.50am onwards.
Several appliances were sent to the scene and residents were rescued from six properties.
The A92 was closed following flooding after three cars were stuck in water between Arbroath and Montrose at around 4.10am.
Police said the fire service went to the scene and there were no reports of any injuries.
There was also flooding on the A90 at Toll of Birness in Aberdeenshire.
Police advised motorists to drive with care in the area.
The Met Office warning says that heavy rain will continue through Thursday morning, leading to further accumulations of 0.6in (15mm) for north-east Scotland with a few places perhaps seeing a further 1.2in-1.6in (30mm-40mm).
However it says that the rain will gradually ease later in the morning.
Elsewhere, it will remain mostly dry but the heavy cloud could be enough to bring rain and drizzle.
There are no reported problems on the railways, but some CalMac Ferries are disrupted due to Wednesday’s bad weather.