New investigations of the Southwest Indian and Arctic ridges reveal an ultraslow-spreading class of ocean ridge that is characterized by intermittent volcanism and a lack of transform faults. We find that the mantle beneath such ridges is emplaced continuously to the seafloor over large regions. The differences between ultraslow- and slow-spreading ridges are as great as those between slow- and fast-spreading ridges. The ultraslow-spreading ridges usually form at full spreading rates less than about 12 mm yr(-1), though their characteristics are commonly found at rates up to approximately 20 mm yr(-1). The ultraslow-spreading ridges consist of linked magmatic and amagmatic accretionary ridge segments. The amagmatic segments are a previously unrecognized class of accretionary plate boundary structure and can assume any orientation, with angles relative to the spreading direction ranging from orthogonal to acute. These amagmatic segments sometimes coexist with magmatic ridge segments for millions of years to form stable plate boundaries, or may displace or be displaced by transforms and magmatic ridge segments as spreading rate, mantle thermal structure and ridge geometry change.