A constructive analytic function f is defined as a pair of form $(A,\Omega)$, where $A$ is a fundamental sequence in some constructive metric space and $\Omega$ is a regulator of its convergence into itself. The pointwise-defined function $f$ corresponding to function $f^*$ turns out to be Bishop-differentiable [2], while the domain of $f^*$ is the limit of a growing sequence of compacta. The derivative of a constructive analytic function and the integral along a curve are defined approximatively. It is proved that the fundamental theorems of constructive complex analysis are valid for such functions. Eight items of literature are cited.