  In this article, we introduce a conditional marginal model for longitudinal
data, in which the residuals form a martingale difference sequence. This model
allows us to consider a rich class of estimating equations, which contains
several estimating equations proposed in the literature. A particular sequence
of estimating equations in this class contains a random matrix
$\mathcal{R}_{i-1}^*(\beta)$, as a replacement for the ``true'' conditional
correlation matrix of the $i$-th individual. Using the approach of [12], we
identify some sufficient conditions under which this particular sequence of
equations is asymptotically optimal (in our class). In the second part of the
article, we identify a second set of conditions, under which we prove the
existence and strong consistency of a sequence of estimators of $\beta$,
defined as roots of estimation equations which are martingale transforms (in
particular, roots of the sequence of asymptotically optimal equations).
