  We collect, survey and develop methods of (one-dimensional) stochastic
approximation in a framework that seems suitable to handle fairly broad
generalizations of Polya urns. To show the applicability of the results we
determine the limiting fraction of balls in an urn with balls of two colors. We
consider two models generalizing the Polya urn, in the first one ball is drawn
and replaced with balls of (possibly) both colors according to which color was
drawn. In the second, two balls are drawn simultaneously and replaced along
with balls of (possibly) both colors according to what combination of colors
were drawn.
