  We study U(1) and U(2) instanton solutions on noncommutative R^4 based on the
noncommutative version of ADHM equation proposed by Nekrasov and Schwarz. It is
shown that the anti-self-dual gauge fields on self-dual noncommutative R^4
correctly give integer instanton numbers for all cases we consider. We also
show that the completeness relation in the ADHM construction is generally
satisfied even for noncommutative spaces.
