It is a maxim of orchestra management that when you hire a new music director, you should immediately start looking for the next one.

Gustavo Dudamel arrives this fall as the New York Philharmonic’s music director designate, then as its music and artistic director in the 2026-27 season. No one is looking to replace him quickly, but even with an incoming superstar, any orchestra’s responsibility is to keep casting around for rising talent — to see who has chemistry with the players, who is worthy of being invited back and who might even be an intriguing candidate for a hopefully well-in-the-future opening.

The new year has brought some of this new blood to the podium at David Geffen Hall, with back-to-back debuts from two maestros in their 40s, of the same generation as Dudamel. I heard them on back-to-back evenings: Kevin John Edusei on Tuesday and Daniele Rustioni on Wednesday.

Both concerts were excellent. The Philharmonic has emerged from its holiday break sounding fresh and vigorous, yet open to a pair of conductors clearly interested in drawing out subtleties.

Edusei’s debut was perhaps the more impressive achievement, since this German musician, who is finishing a term as principal guest conductor of the Fort Worth Symphony Orchestra in Texas, was presenting a program of pieces that can be difficult to put across. Strauss’s “Also Sprach Zarathustra,” like all this composer’s tone poems, can come off leaden and overlong. Berlioz’s set of six songs “Les Nuits d’Été” can feel too delicate to really register in a big concert hall.

“Zarathustra” is, of course, famous for its swelling, blasting opening, the brass fanfare that Stanley Kubrick used so memorably in “2001: A Space Odyssey.” But much of the half-hour work is not in this triumphal vein; it’s evocative grumbling, chamber-style closeness, eerily murmured music.

The best conductors of Strauss’s tone poems revel in the quieter stuff, rather than seeming to just wait impatiently for the next blaring climax. If you relish this material, as Edusei did, those climaxes build more naturally and powerfully. On Tuesday, the constantly changing, all too easily meandering piece came off as tauter than usual; it wasn’t forced, but it did feel focused. Strauss’s roguish grotesqueries were beautifully played, with warm coziness to the thicket of intertwining lines in the winds.

In “Les Nuits d’Été,” Berlioz’s wistful settings of love poems, the mezzo-soprano Isabel Leonard was a superb soloist. She sounded silky yet rich, her tone in “Sur les Lagunes” dusky and melancholy, with the seductive illusion of arriving from a distance. She captured the longing stillness of “Absence,” but also the insouciance of the first and final songs. The orchestra was stylish and specific: misty yet precise in “Au Cimitière,” with a sense of nocturnal intimacy throughout.

Edusei’s concert began with Samy Moussa’s “Elysium” (2021), a glacially evolving, bombastically stirring 12-minute piece that the Philharmonic played with cinematic radiance. There was an opener of the same length on Rustioni’s program, which continues through Saturday, but it’s a rarity from the past rather than something contemporary.

Mario Castelnuovo-Tedesco’s restless “Merchant of Venice” Overture (1933) hadn’t been performed by the orchestra since 1941, so it was fascinating to hear this confidently woven mixture of forcefully dramatic and gracefully dreamlike music.

Rustioni is an Italian conductor best known in opera; he was recently named the Metropolitan Opera’s principal guest conductor. But he is doing ever more concert work, particularly in the United States, and capped his admirable debut with an exciting rendition of Tchaikovsky’s Fourth Symphony, one of the pillars of orchestral repertoire.

As in the Castelnuovo-Tedesco overture, Rustioni guided the transitions of the Tchaikovsky in a way that was dramatic without being overstated. There were passages in the first movement that initially struck me as overly slow, but Rustioni confidently — indeed, thrillingly — increased the tempo little by little, negotiating the score without abruptness or awkwardness and growing to a scorching dash at the end of the movement.

The second movement was deliberately paced yet coiled with restrained energy; the lyricism felt expansive without losing forward momentum. The celebration of the third and fourth movements felt honestly earned, with the orchestra seeming to enjoy its full dynamic range.

Before intermission, in Dvorak’s Violin Concerto, Joshua Bell handled the solo part with his usual preternaturally smooth tone and his usual odd lack of surprise despite surface liveliness. He blended especially well with the winds in the first movement. In the second, the strings played with heated unanimity, and the third was lively yet elegant, not too rustic or heavy. Even with a certain pretty emptiness at its center, the concerto was polished and enjoyable.

While Dudamel is on his way, it is reassuring that the Philharmonic isn’t using his hiring to rest on its laurels. We can only hope that the relationships it is beginning now with artists like Edusei and Rustioni will continue and deepen.