  The additive model is one of the most popular semiparametric models. The
backfitting estimation (Buja, Hastie and Tibshirani, 1989, \textit{Ann.
Statist.}) for the model is intuitively easy to understand and theoretically
most efficient (Opsomer and Ruppert, 1997, \textit{Ann. Statist.}); its
implementation is equivalent to solving simple linear equations. However,
convergence of the algorithm is very difficult to investigate and is still
unsolved. For bivariate additive models, Opsomer and Ruppert (1997,
\textit{Ann. Statist.}) proved the convergence under a very strong condition
and conjectured that a much weaker condition is sufficient. In this short note,
we show that a weak condition can guarantee the convergence of the backfitting
estimation algorithm when the Nadaraya-Watson kernel smoothing is used.
