A releasable hanging system having a loop fastener component and a hook fastener component. The loop fastener component includes a flexible patch carrying a field of engageable fibers exposed on a front side of the patch and an adhesive on a back side of the patch. The hook fastener component includes a resin base carrying an array of male touch fastener elements. A significant majority of the male touch fastener elements each extend from the base to a distal tip to overhang the base in a single, common direction. The fastening system can be used to hang an object on a vertical surface such that the male touch fastener elements of the significant majority bear the weight of the object in a downward direction, and such that the significant majority of the male touch fastener elements are oriented so as not to inhibit lifting of the object in an upward direction.