  The paper continues the authors' work on the adaptive Wynn algorithm in a
nonlinear regression model. In the present paper it is shown that if the mean
response function satisfies a condition of `saturated identifiability', which
was introduced by Pronzato \cite{Pronzato}, then the adaptive least squares
estimators are strongly consistent. The condition states that the regression
parameter is identifiable under any saturated design, i.e., the values of the
mean response function at any $p$ distinct design points determine the
parameter point uniquely where, typically, $p$ is the dimension of the
regression parameter vector. Further essential assumptions are compactness of
the experimental region and of the parameter space together with some natural
continuity assumptions. If the true parameter point is an interior point of the
parameter space then under some smoothness assumptions and asymptotic
homoscedasticity of random errors the asymptotic normality of adaptive least
squares estimators is obtained.
