If the question is limited to royal dynasties,

and, if definitions are:

"Oldest" = dynasty which became monarchs earliest;

"Surviving" = still reigning as monarchs;

"Dynasty" = unbroken line of male descent;

Then I believe the oldest surviving European dynasty is the Bernadotte dynasty of the Kings of Sweden, starting with King Karl XIV Johan, who became King in 1818, and continuing through 5 further kings before arriving at King Carl XVI Gustaf, who became King in 1973, and is still King today.