BERLIN — Since its founding, the Berlin State Opera has lived through a monarchy, two republics and two dictatorships. It is used to strong leaders. On Thursday, when the institution celebrated its 275th birthday with a concert in its newly renovated theater on this city’s central Unter den Linden boulevard, it did so against the backdrop of a new situation: political limbo.

In a welcome address made from the stage, the opera house’s director, Jürgen Flimm, alluded to Chancellor Angela Merkel’s inability to form a governing coalition since her party’s meager victory in the elections held in October. Still, he quipped, things seemed to be working just fine.

One thing working very well indeed is the music-making of the State Opera’s orchestra, the Staatskapelle Berlin. In works by Mendelssohn, Boulez and Richard Strauss, the ensemble’s music director, Daniel Barenboim — who also holds the same position in the opera house — drew a burnished and vigorous sound from the orchestra and playing that was confident and free.