  A noncommutative algebra of the complex $q$-twistors and their differentials
is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real
and pseudoreal $q$-twistors are discussed too. We consider the quantum-group
self-duality equation in the framework of the local gauge algebra of
differential forms on $q$-twistor spaces. Quantum deformations of the general
multi-instanton solutions are constructed. The corresponding noncommutative
algebras of moduli are introduced. The general $q$-instanton connection is a
function of the $q$-twistors and the $q$-moduli .
