Hilla Rebay, the abstract artist and the first director of the Museum of Non-Objective Painting (now the Solomon R. Guggenheim Museum), was as important to the reception of Modern art and abstraction in America as Alfred H. Barr Jr., the first director of MoMA. An imaginative though minor painter herself – her work was derivative of Malevich, Schwitters, and Kandinsky – she championed Arp, Kandinsky, Klee, Mondrian, the Delaunays, Leger, Auguste Herbin, and Ilya Bolotowsky. Yet she also idolized such academic painters as Rolph Scarlett and her one-time lover Rudolf Bauer, who made a career doing mediocre pastiches of Kandinsky.

Two current exhibitions, “Hilla Rebay and the Museum of Non-Objective Painting” at DC Moore Gallery and “Art of Tomorrow: Hilla Rebay and Solomon R. Guggenheim” at the Guggenheim, are devoted to Rebay, the artists she championed, and her connection to Guggenheim and his museum, which she was instrumental in founding. Together these two uneven shows, comprised of more than 250 works (roughly 175 by Rebay), give us a pretty good overview not only of Rebay’s shaky trajectory as a painter, but also of her uneven taste as a museum director and collector. In terms of the advancement of non-objective art, Rebay remains one of the most important emigres to come to America during the first half of the 20th century – and she was a much better adviser than the Guggenheim show makes her out to be.

The German-born Rebay (1890-1967) studied art in Munich, Berlin, and at the Academie Julian in Paris. In Zurich she met Jean Arp, with whom she became romantically involved. Arp introduced her to the Cabaret Voltaire and to the work of Kandinsky, Klee, Chagall, Marc, and Bauer. Rebay read Kandinsky and began working abstractly. She showed with Dada artists, and created some gorgeous collages and prints, some of which were used for Dada and Der Strum catalogs, and many of which are on view at the Guggenheim. In 1919 she returned to Berlin with Bauer, where she met

Max Ernst, Kurt Schwitters, and Erich Mendelsohn, and she made a living as a portrait painter.

In 1927 she moved to New York, where she gave painting lessons to Louise Nevelson, commissioned portraits, and hobnobbed with Gertrude Vanderbilt Whitney and the Guggenheims. She painted Solomon R. Guggenheim’s portrait in her studio (a work also at the Guggenheim), where Guggenheim saw non-objective works by Rebay and other European artists. During those sittings, so the story goes, she convinced Guggenheim to begin collecting abstract art.

In no time, she became Guggenheim’s adviser, introducing him to Chagall, Kandinsky, Delaunay, Leger, and Laszlo Moholy-Nagy – and his collection of abstract art began. In 1933 Rebay convinced Guggenheim that he needed a museum to house his collection, but it was not until 1939 that the Museum of Non-Objective Painting opened at 24 East 54th Street.

Rebay would direct the museum until 1952, when it was renamed after Guggenheim. In 1943 she considered several architects, among them Walter Gropius and Le Corbusier, to design a “temple” to non-objective painting, but she settled eventually on Frank Lloyd Wright, whose building on Fifth Avenue opened in 1959.

Visitors to “Art of Tomorrow” (the first museum show dedicated to Rebay’s entire career) may be reminded of the 1996 Guggenheim exhibition “Abstraction in the Twentieth Century,” which appears to be the seed for the current exhibitions. In that show, a gallery was devoted to Rebay’s original Museum of Non-Objective Painting. That show highlighted the great Kandinskys and the horrible Bauers that Rebay brought to America.

“Abstraction in the Twentieth Century” was a monumental disappointment, not only because of what it put in but also because of what it left out. It was a missed opportunity to give us a real sense of the myriad approaches to abstraction that have developed since the early seeds were planted around 1912. “Art of Tomorrow,” though densely packed with more than 200 works – ephemera, sketchbooks, photographs, paintings, drawings, and letters; some of them masterpieces, many of them mediocre – though exciting and engaging in places, is a similar kind of letdown. It, too, feels like a missed opportunity.

First of all, the overcrowded show is relegated to three spaces on three separate floors in the cramped side galleries off Wright’s rotunda. This backroom arrangement, in which the works on paper are separate from most of the paintings, does not allow for adequate comparison of the works. Nor does it offer a sense of Rebay’s artistic development or of flow from work to work.

This show, if it had been taken more seriously, should have been overflowing with the great abstract paintings Rebay and Guggenheim were responsible for adding to the museum. As it is, there is only one Arp collage, one Klee watercolor, one Schwitters. In terms of paintings, there is only one Moholy-Nagy, one Leger, and half a dozen Kandinskys, each matched one-to-one by a Bauer. (The show at DC Moore is a little more evenhanded, with two beautiful Bolotowskys.) “Art of Tomorrow” should have taken over the whole rotunda. Instead, it feels more like a footnote or a nod to the origins of the Guggenheim, rather than a full engagement with the artists who made the museum.

“Art of Tomorrow” begins with Rebay’s solid oil on linen “Self-Portrait” (1909-10). It then moves into some of the most exciting works she ever did: the early, obsessive, small abstract watercolors, oils, and collages. Some of these dynamic works rely too heavily on Kandinsky, Marc, or Klee; others feel heavily inspired by Japanese prints; just the same, there is fluttering delicacy and light in a few of them that made me want to get closer.

Part of the allure of Rebay as an artist is knowing what fed her. You can see all kinds of influences in her paintings and drawings, not only the work of other abstract painters but also of fashion illustration, the movements of animals, photomontage, and Diaghilev’s Ballets Russes. Often Rebay’s vocabulary feels borrowed rather than found, felt, or genuine.

This is especially true of the large paintings, which generally feel undercooked and do not breathe or open up, and in which the grounds, as in Bauer’s works, have little tension. In the large works by both Bauer and Rebay, the forms can tend to feel decorative and inert, as if they had been painted somewhere else and pasted onto the canvas. Yet Rebay’s impressive range – from strange, almost racist, black dancers to Kirchner-esque figures to straight-ahead portraits to Kandinsky-esque cosmoses – conveys an overwhelming energy, love, and enthusiasm for painting.

It is this infectious enthusiasm that comes through in both exhibitions, which are must-sees for anyone interested in abstract painting; and it is this love and enthusiasm to which the current Guggenheim owes its very existence.

“Art of Tomorrow” until August 10 (1071 Fifth Avenue, at 89th Street, 212-423-3500).

“Hilla Rebay and the Museum of Non-Objective Painting” until June 24 (724 Fifth Avenue, between 56th and 57th Streets, 212-247-2111).