The paper studies the problem of closed loop adaptive noise cancellation, namely the situation in which an unknown dynamics affects the ``cancelling signal''. The nature of the limit points of the mean limit ordinary differential equation associated to a suitably contrained stochastic approximation algorithm is investigated and, under appropriate conditions, it is shown that, for increasing dimension of the weight vector, the limit points converge to the optimal (infinite-dimensional) weight vector. Furthermore, the algorithm is a stochastic gradient descent algorithm and leads to a nearly optimal solution.