Storms Elsa and Fabien have flooded rivers, brought down power lines, uprooted trees and disrupted rail and air travel across the region, leaving more than 118,000 households without electricity.
Two people have so far died in Portugal and seven have now been killed in Spain, the worst affected country, after a fisherman was swept off rocks into the sea in Catalonia.
The local government said three police officers and another fisherman had to be rescued after they tried to save the man in the resort town of Sant Feliu de Guxols, 100 kilometres (70 miles) northeast of Barcelona.
The deaths in Spain include a South Korean woman killed by debris falling from a building in Madrid and a Dutch man who drowned windsurfing in rough weather off the Andalusian coast.
As a weakened Storm Elsa moved over Britain on Saturday, Storm Fabien quickly moved in, bringing winds of 170 kilometres per hour to Galicia in northwestern Spain, forcing the cancellation of 14 flights according to Spanish airport operator Aena.
Some 8,000 households in Galicia were without power due to damage caused to power lines by the wind, local officials said. Eight Madrid city parks remained shut on Saturday because of the strong winds.
However, Spanish officials said on Sunday that Fabien was moving away quickly. Parks and cemeteries were also closed in Bordeaux in southwestern France on Saturday while the Arlette Gruss circus, which had set up in a big tent in the city’s main square, cancelled three performances.
France’s weather office placed 15 regions in the southwest of the country on orange alert Saturday, as the storm battered its Atlantic coast.
The winds were as fast as 148 kph at Socoa, in the southwest near the border with Spain. Even on the northwest coast of Brittany, winds reached up to 120 kph.