Long-eye heddles have several uses, only one of which (perhaps most commonly known) is on the drawloom, where they are used together with pattern heddles. Almost any other double-harness set up -- smålandsväv, skillbragd, double harness double weave, just to name a few -- all require the use of these long-eye heddles. Weaves such as sword damask, various pick-up techniques, or treadled leno or opphämta using a weaving sword also require a single set of shafts with long-eye heddles.
If you'd like to learn more about drawloom weaving, Becky's DVD Dress Your Swedish Drawloom contains the most comprehensive instructions to be found. Or, even better: come take one of our Drawloom classes!