  We introduce a recursive algorithm of conveniently general form for
estimating the coefficient of a moving average model of order one and obtain
convergence results for both correct and misspecified MA(1) models. The
algorithm encompasses Pseudolinear Regression (PLR--also referred to as AML and
$RML_1$) and Recursive Maximum Likelihood ($RML_2$) without monitoring.
Stimulated by the approach of Hannan (1980), our convergence results are
obtained indirectly by showing that the recursive sequence can be approximated
by a sequence satisfying a recursion of simpler (Robbins-Monro) form for which
convergence results applicable to our situation have recently been obtained.
