  Under a nonlinear regression model with univariate response an algorithm for
the generation of sequential adaptive designs is studied. At each stage, the
current design is augmented by adding $p$ design points where $p$ is the
dimension of the parameter of the model. The augmenting $p$ points are such
that, at the current parameter estimate, they constitute the locally D-optimal
design within the set of all saturated designs. Two relevant subclasses of
nonlinear regression models are focused on, which were considered in previous
work of the authors on the adaptive Wynn algorithm: firstly, regression models
satisfying the `saturated identifiability condition' and, secondly, generalized
linear models. Adaptive least squares estimators and adaptive maximum
likelihood estimators in the algorithm are shown to be strongly consistent and
asymptotically normal, under appropriate assumptions. For both model classes,
if a condition of `saturated D-optimality' is satisfied, the almost sure
asymptotic D-optimality of the generated design sequence is implied by the
strong consistency of the adaptive estimators employed by the algorithm. The
condition states that there is a saturated design which is locally D-optimal at
the true parameter point (in the class of all designs).
