Gain the southern Gelmerlücke from Mittlist Diechter - a granite bench below the hut with a creek. At high water, this crossing requires great care. Red markings point the way, which is at first a trail, turning into a scramble and eventually becoming a series of chimneys and gullies (UIAA III to III+) with much loose rock and dirt.
From the notch, continue on the South Ridge of the Chlys Gelmerhorn, occasionally going into the east face. Beautiful climbing in UIAA III (5.3 to 5.4). The final summit plates offer some fun UIAA IV (5.5-ish) climbing on fine holds.
Rappel from the summit block 15m and then again 30 m to the Gelmerlücke. (If necessary one can continue rappelling twice more 20m to escape back to Mittlist Diechter.) It is now a very easy traverse over to the Großes Gelmerhorn (UIAA II ).
If done in reverse (N to S), the climb is UIAA V- (5.8)
From the summit of Großes Glemerhorn, one down climbs over ledges in the west flank to the north. Several rappels (rings in place) and some more down climbing take you to the North Gelmerlücke. From the notch rappel another 20 m to a shoulder. Down climb from there 150 m to a grassy flank and follow the steep and often slippery trail back to Mittlist Diechter. 6 to 7 hours hut to hut.
From the North Gelmerlücke notch, it is possible to continue the traverse along one, more or all of the Gelmerspitzen.
Much protection is in place, but along with 5 quickdraws, one should have a small rack, about 10 carabiners and some slings. 50 M rope is adequate.
No snow or glacier is crossed.