Plants solitary or in compact, or sometimes loose, tufts, (usually wholly purple, sometimes green), not stoloniferous, not rhizomatous, with caudex. Leaves basal and cauline, (cauline 1-3, dissimilar from basal, reduced); petiole ± flattened, (2-)5-35 mm; blade reniform to orbiculate, (2-)3-5(-7)-lobed (lobes rounded), (2-)3-6(-10) mm, thin or slightly fleshy, margins entire, eciliate or sparsely stipitate-glandular, (inconspicuous nonsecreting hydathodes sometimes present), apex acute, surfaces glabrous or sparsely hairy. Inflorescences 2-5-flowered cymes, sometimes solitary flowers, 1-5 cm, tangled, purple-tipped stipitate-glandular; bracts petiolate. Flowers: (hypanthium U-shaped in longisection, sparsely to densely long stipitate-glandular); sepals erect, (sometimes purple), ovate to lance-oblong, (1.5-2.1 mm wide), margins eciliate, surfaces ± stipitate-glandular; petals purple or white, often midvein ± purplish, faded when dried, not spotted, oblong, (1.5-)2-3.4(-5) mm, equaling or to 1.5 times sepals; ovary 1/2 inferior. 2n = 26. Flowering summer. Wet tundra, open gravel and silt, stream and lake margins, snow beds, shady ravines and cliffs, seepage under rocks, silty and gravelly seashores; 0-3000+ m; Greenland; Alta., B.C., Man., Nfld. and Labr. (Labr.), N.W.T., Nunavut, Que., Yukon; Alaska, Ariz., Calif., Colo., Idaho, Mont., Oreg., Wash., Wyo.; n Asia; Atlantic Islands (Spitsbergen). Reports of Saxifraga hyperborea from Mount Washington, New Hampshire (e.g., Á. Löve and D. Löve 1964) require confirmation; all specimens examined from this location appear to be S. rivularis. C. L. Hitchcock (1961) treated all western material as S. debilis, including that of the Pacific Northwest that is included here. For Colorado, W. A. Weber (1990) appears to have applied the name S. rivularis to what we call S. hyperborea, and S. hyperborea subsp. debilis to what we call S. debilis. P. K. Holmgren and N. H. Holmgren (1997) included under their broad concept of S. rivularis both S. hyperborea and S. debilis, noting that the plants had gone usually under the latter name. Both species are present in the Rockies and the Intermountain Region. In northeastern North America, Saxifraga hyperborea and S. rivularis are often sympatric, although the latter is absent from the extreme north. The major distinguishing feature between diploid S. hyperborea and tetraploid S. rivularis is the presence of rhizomes in the former and their absence in the latter (see key), a character that is sometimes difficult to interpret on herbarium sheets. Plants of S. hyperborea are usually smaller (2-5 cm) and reddish (sometimes green), with usually three- to five-lobed leaves and petals about one and one-half times longer than sepals, while plants of S. rivularis are taller (5-10 cm) and usually green (although sometimes reddish, particularly in the western var. arctolitoralis), with usually five-lobed leaves and petals two to three times longer than sepals.