“Painting: Now and Forever, Part II,” a group show occupying both the Matthew Marks and Greene Naftali galleries, refers back to a survey of contemporary painting (Part I) held a decade ago at Marks and the now defunct Pat Hearn Gallery. At the time, when painting was considerably more embattled and the market for it much smaller, the show’s title rang defiant; today, it sounds ironic. Part II explores a medium — or approach, since the paint is often absent here — in a state of productive entropy; it is painting that pushes at whatever limits are left.

The show pushes harder against those limits at Greene Naftali than at Matthew Marks, though both venues offer a mix of the very contemporary with a few historical works that continue to exert an influence. At the former, a small, ugly mishmash of red and purple and green called “Towards an Abstract Icon” (1980), by Paul Thek, prefaces the current naïve style. To establish a suitably tongue-in-cheek context for this canvas, Mr. Thek set it in a gold frame, replete with a viewing light. This sort of wide-angle art, in which the frame as well as the canvas constitute the work, took hold in the early ’80s and, by our time, has generated enough branches of ironic painting to fill out a bush.

So in 1981, William Leavitt hung an intentionally pedestrian painting of a blue sea creature on a wall of faux-wood paneling, left a potted plant on the floor in front of it, and called the whole thing “Manta Ray.” In 2003, Mike Kelley reversed the procedure. Instead of calling the room with the painting the work, he made a little piece of the room his focus, framing a square swath of carpet doused in orange acrylic and calling it “Carpet #2.”

Cosima von Bonin dispenses with the paint altogether in her wonderful “Straight, No Chaser” (2007), in which patterned pieces of fabric, affixed to a canvas, form a hard-edged abstract background for a small drawing sewn with white thread. “Moving Circus” (2008) retains the paint but removes the canvas and stretcher. This flag-like work, by Kai Althoff and Erin Allen, consists of interlocking “L”s of blue and red fabric decorated with tempera paints as well as strips of gauzy gray fabric. Unlike the Bonin, the effort in this one seemed as limp as its materials.

Among the best of the unpainted paintings is Kelley Walker’s untitled screen print on canvas, in which convincing brickwork floats atop images of USA Today pages, from May 27, 2008. Among the blandest are the gloppy versions of the Mona Lisa done by the art collective Gelitin, heavily built up in plasticine on wood. The world might still need to investigate the limits of painting, but it surely doesn’t need another Mona Lisa joke.

And what is Ellsworth Kelly’s elegant “Green Relief” (2007) — an allover green canvas askew atop an allover white one — doing in such raucous company? Although the work here is recent, Mr. Kelly represents a historical precedent for two current, and at times related, tendencies in painting. One is toward treating the picture as an object, like sculpture, as in the Althoff and Allen contribution. The other is toward hard-edged abstraction drained of its Modernist theoretical justification, as in Sergej Jensen’s “Werewolf” (2003), a brownish allover rectangle with a bespeckled (the work uses oil paint and saffron) yellow oblique triangle at the left side.

At Matthew Marks, the Reena Spaulings piece “Enigma 15” (2008) gestures at both tendencies. It offers a square swath of white tablecloth from a recent art-world dinner with the leftover stains as its “imagery.” But on the whole, the work at Marks seems quieter, and certainly more blue-chip. The precursors here are not seldom-seen artists’ artists, such as Thek, but names bloated with market value, such as Martin Kippenberger, here representing naïve-style “ugly” painting, and Blinky Palermo, who’s on the abstraction-without-ideas team.

Recently made pretty, or not so pretty, abstractions — by Daan van Golden and Charline von Heyl, among others — outnumber the limit-testing works. And when they are included, the more challenging pieces at Marks are likely to seem declawed for fine living rooms. Thus, Katharina Fritsch’s “Picture with Mirror” (1998), a rectangular mirror in a gorgeous frame, seems more decorative than daring. Ditto “Boston Store” (2008), a throwaway by the talented Mathew Cerletty, in which an abstract logo atop the title words are carefully rendered in oils. Wade Guyton’s untitled black “X”s and arrows, all ink-jet prints on linen, retain their house-kitty claws, but do not necessarily require a room of their own, as they’re given here.

Still, the theme of paintings prodding the notion of painting holds up sturdily in both venues. And for those who wonder why such ironic works stand for painting now, there’s another, less impish way to read this show’s title: Painting is now and will forever be going through some point in the cycle of destruction and rebuilding. Artists always destroy what was with what is. If the territory of “Part II” is by now well trodden, the vistas offered are, at least, sufficiently exciting to justify the trip.

Until August 15 at Matthew Marks (523 West 24th Street, between Tenth and Eleventh avenues, 212-243-0200) and Greene Naftali (508 West 26th Street, at Tenth Avenue, 212-463-7770).