NEW YORK — The hallmark of a truly inspired stage actor may not be what he or she does with outstanding material, but what they can accomplish with the run-of-the-mill stuff.

By that measure, a sustained ovation is due Jake Gyllenhaal for his yeoman work in “Sea Wall/A Life,” a pair of rather humdrum monologues by British playwrights Simon Stephens and Nick Payne that made it to Broadway — chiefly, it appears, because the popular Gyllenhaal is in one of them.

The first piece, “Sea Wall,” features Tom Sturridge offering a mannered, mournful account of the death of a child. The second monodrama, “A Life,” has the preternaturally charming Gyllenhaal narrating the intertwined stories of a baby’s birth and an old man’s death. The double bill, which had its official opening Thursday at the Hudson Theatre, is on the whole an innocuous excursion into the personal traumas and pinnacle family events that compel a man-child to become a man.

The monologues, each about 45 minutes, are well-composed, solemnly heartfelt testaments to bracingly emotional experiences. They remind you of first-person articles about manhood that crop up regularly in sensitive men’s magazines. Largely descriptive, the narratives don’t reveal much that you haven’t read or heard before. So director Carrie Cracknell does what she can to up the artiness quotient, posing the actors in intense arcs of light and giving them little extra chores, like flipping the big on-off switch for the house lights, and wandering in the audience.

Sturridge tells the sadder tale, an unvarnished memory of a young daughter and a terrible accident on a French beach, the kind of dread scenario lurking in every parent’s head. If there’s any admirable heft to the monologue, it’s in the lack of judgment that the British storyteller, a young married man named Alex, applies to the tragedy. He’s had to accept his unspeakable misfortune, and there’s a dignity and a grace in the restraint with which he’s able to speak about it.

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The actor attempts to imbue Alex with some comic idiosyncrasies, such as the habit of invoking the names of French places with an emphatic gesture and a thick French accent. This is conveyed in such a theatrical way that an audience isn’t sure what he’s going for, and it renders the character as peculiar. The resulting inaccessibility makes him less, not more, interesting.

Gyllenhaal’s Abe in “A Life” is the veritable open-book counterpart to Sturridge’s Alex in “Sea Wall.” The birth of Abe’s first child and the earlier death of his father form the narrative spine of his story. What’s remarkable is not so much the details Abe imparts as the way Gyllenhaal imparts them. As he has shown in previous vorays on the stage in New York — in Stephen Sondheim and James Lapine’s “Sunday in the Park With George,” for instance, and the far better two-hander by Nick Payne, “Constellations,” Gyllenhaal has that ineffable gift for instant emotional intimacy, the ability to make you believe you’re seeing his character from the inside out.

That, for many people, is worth the price of admission. I enjoyed what this adventurous actor brought to this routine, fairly rudimentary exercise, but next time, I’d like to see him in something that really makes him sweat.

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Sea Wall/A Life, by Simon Stephens and Nick Payne. Directed by Carrie Cracknell. Set, Laura Jellinek; costumes, Kate Voyce and Christopher Peterson; lighting, Guy Hoare; sound, Daniel Kluger; projections, Luke Hall; original music, Stuart Earl. About 2 hours. $59-$339. At the Hudson Theatre, 141 W. 44th St., New York. 855-801-5876. thehudsonbroadway.com.

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