Collaboration between large Washington arts institutions is painfully rare. When the National Gallery of Art presented an exhibition devoted to Diaghilev and the Ballets Russes in 2013, the Kennedy Center remained mostly indifferent to the fact that one of the greatest chapters in music and dance history was being explored less than three miles away.

So it’s good news that the Phillips Collection and the Hirshhorn Museum have pulled together a joint exhibition of the paintings of Markus Lüpertz, an important postwar German artist who has never been the subject of a major museum survey in the United States. Even better than the collaboration itself is the distinct difference in approach taken by each museum, which highlights two distinctly different ways of approaching the artist.

At the Hirshhorn, the approach is methodical and focused. Blessed with galleries far larger than those at the Phillips, the Hirshhorn is showcasing Lüpertz’s paintings from the 1960s and ’70s, some of them room-filling, ominous ecstasies of color. Wall texts lay out his basic themes and motifs, from strange meditations on Donald Duck and the “tent paintings” in the 1960s to later works that took up symbols from Germany’s Nazi past, and repurposed them as surreal “dithyrambs,” a term borrowed from Greek poetry but reinvented by Lüpertz as a catchall for his not-quite-abstract forays into abstraction and not-quite-figurative exercises in drawing real things in the world.

[Kennicott on George Condo at the Phillips Collection, closing June 25]

At the Phillips Collection, there is hardly any wall text, and no strict chronological order. The artist suggested this arrangement that roams freely over his career, including major works exploring mythological and historical themes made in the past few years. The hang is associative and provocative and avoids explicit comment on the what or the why of Lüpertz’s art.

This is, no doubt, how Lüpertz prefers it. The 76-year-old artist has spent his career at odds with the larger trends of German postwar art, devoted to painting while much of the art world’s creative energies went into conceptual art, performance and video. Not only has he been consistently loyal to painting, and in a style that acknowledges his interest in the great painters of the past, he has also resisted the magnetic pull of total abstraction. His work seems to orbit the real world of things — things like tents, landscapes, and military uniforms — but without ever quite arriving there. Abstraction, for Lüpertz, is an energy, not a dogma. It keeps him in motion, like a satellite spinning around but never plunging into a planetary body.

He also subscribes to an enchantingly hermetic notion of humanism. He is convinced that painting is an intellectual activity, that it helps us see things that would otherwise be imperceptible, and that it improves the world. But he will not say exactly how, as if to define the moral operation of art would neuter its power.

“Painting does not educate the person looking at it,” he says in a series of questions and answers that function as a manifesto posted on the wall at the Phillips Collection. “It takes the viewer seriously and ennobles him by assuming an intellectually emancipated world.” And: “[The painter] is the cultural conscience of his times. The more a period allows great painters to exist, the more civilized it is.”

Armed only with Lüpertz’s manifesto, visitors to the Phillips Collection will likely come away with the sense that he is an artist primarily involved with the internal dynamics of the art form, making paintings about paintings. Or as he has said: “What I paint is a chain of things; one painting leads to the next. A detail in one painting, a cascading chip, can already be the next image.” Some of his works, including his “Beautiful Objects” of 1978, recall Picasso, and perhaps Max Beckmann is in the background of some of the more well-mannered forays into expressionism. Willem de Kooning, Jean Dubuffet and Paul Cézanne seem close at hand elsewhere.

But the German references are startling, and hard to process. What are those stahlhelms — the steel helmet so evocative of German militarism — doing in two paintings from 2009, one upturned and seen in silhouette against a bleak landscape, the other glinting in the sun with fertile fields in the background?

[Long lines for Kusama make for a distracted, frenetic experience of art]

If you believe Lüpertz, they may be merely the sort of detail that leads from one painting to next, links in the “chain of things” migrating through his art. But clearly that’s not the case. No German artist who speaks about art and civilization as Lüpertz does can deploy these visual themes as neutral details. Their power is so explosive that they undermine his profession of faith in abstraction.

Visitors who experience the Hirshhorn exhibition first will have a stronger sense of Lüpertz’s relation to history, and the art world. He is grappling with things like Pop Art, and the larger German critique not just of its Nazi past, but of its capitalist present. His tent paintings don’t indulge the American fetish for brand names, but they are irreverent like Pop painting, and evoke a broader world of cheap, impermanent things, a restless culture on the move, a society that leaves its mark not through grand edifices but through an accumulation of ephemera and trash.

The German motives are gathered together at the Hirshhorn in a room that becomes powerful and oppressive. A series of dithyrambs, called Cyclops I, II and III, from 1973, are some of the most powerful works in either exhibition, reminiscent of late Lovis Corinth, another unclassifiable German painter, who died in 1925.

So which exhibition should you see first? If you are intolerant of a certain amount of bewilderment, then start with the more straightforward Hirshhorn show, which serves as a concise introduction to the artist. But a certain amount of bewilderment is, of course, essential to the essence of an aesthetic experience, so if possible, see the more impressionistically organized Phillips Collection before the Hirshhorn. The paintings are not so large or so assertive, but the episodic and discursive arrangement allows one to experience Lüpertz’s work free of the very things he would like it to be free of.

At the Phillips, you will detect an artist driven by an overwhelming need to paint, without being too much caught up in the life, meaning or history of the things depicted. At the Hirshhorn, you will find an artist who is, in fact, interested in those things, canny about the subjects he chose, and not at all indifferent to the meanings and messages carried by the objects he represented. Both understandings are true, which is what makes this collaboration so valuable: By pursuing two different perspectives, the Hirshhorn and the Phillips have constructed an intriguingly complex picture of a complicated artist.

Markus Lüpertz: Threads of History is on view at the Hirshhorn Museum through Sept. 10; Markus Lüpertz is on view at the Phillips Collection through Sept. 3. For more information, visit hirshhorn.si.edu and phillipscollection.org.