Abstract: An abrasive material is proposed which is useful for the precision treatment of surfaces. This material may be in the form of an abrasive layer adhered by chemical and/or physical bonds to a carrier, the latter preferably made of a flexible material such as plastic. Alternatively, the abrasive material may be in the form of a free abrasive without a carrier. The abrasive material may be in the form of a vacuum condensate consisting of at last 80 atomic percent of an ultradispersed composite superhard diamond-like substance, preferably containing carbon, and including not more than 0.1 atomic percent hydrogen and oxygen, combined. The abrasive material is preferably obtained from the pulse-flows of an accelerated electroerosive plasma.