We　study　the　stabilization　the　wave　equations　with　variable　coefficients　in　a　bounded　domain　and　nonlinear　boundary　feedback　with　time　dependent　delay.　By　the　Riemannian　geometry　methods　and　a　suitable　assumption　of　delay,　we　obtain　the　exponential　decay　when　the　nonlinear　terms　are　linearly　bounded　and　a　general　decay　when　the　nonlinear　terms　have　no　upper　growth　bound.　(C)　2014　Elsevier　Inc.　All　rights　reserved.