  A class of new type graded infinite posets with minimal element are
considered. These so called cobweb posets introduced recently by the present
author provide a wide range of new noncommutative prefab combinatorial schema
with characteristic graded subposets as primes. The schema are defined here via
relaxing commutativity and associativity requirements imposed on the
composition of prefabs by the fathers of this fertile concept. The construction
and the very first basic properties of cobweb prefabs are pointed out in what
follows. An another single valued commutative amd associative composision is
also considered.
