  I carefully study noncommutative version of ADHM construction of instantons,
which was proposed by Nekrasov and Schwarz. Noncommutative ${\bf R}^4$ is
described as algebra of operators acting in Fock space. In ADHM construction of
instantons, one looks for zero-modes of Dirac-like operator. The feature
peculiar to noncommutative case is that these zero-modes project out some
states in Fock space. The mechanism of these projections is clarified when the
gauge group is U(1). I also construct some zero-modes when the gauge group is
U(N) and demonstrate that the projections also occur, and the mechanism is
similar to the U(1) case. A physical interpretation of the projections in IIB
matrix model is briefly discussed.
