Heavy rains in Western Europe led to torrents carrying cars the night before and caused houses to collapse.
German authorities say at least 30 people have been killed in North Rhine-Westphalia and 28 in Rhineland-Palatinate.
Belgian media state that eight people were killed in that country.
Rescue efforts are hampered by blocked roads and interruption of telephone and internet traffic.
In Germany, dozens were rescued from the roofs of their houses, with the help of boats and helicopters.
The governor of the province of North Rhine-Westphalia, Mala Dreyer, states that “such a catastrophe has not been seen so far”.
“We have the dead, we have the missing, many are still in danger,” Dreyer told members of the provincial parliament.
In Belgium, the river Vesdre overflowed and flooded the streets of Pepinster, near Liege.
The main roads in the south and east of Belgium were flooded, and all train departures were suspended.
In Liege, a city of 200,000, the Meza River overflowed, prompting authorities to urge citizens to take refuge in several areas.