Comments on Instantons on Noncommutative R^4

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.