We study the mixed initial-boundary value problem for the capillary wave equation: iut+u2u=∂x3/2u,  t>0,  x>0;  u(x,0)=u0(x),  x>0; u(0,t)+βux(0,t)=h(t),  t>0, where ∂x3/2u=(1/2π)∫0∞sign⁡x-y/x-yuyy(y) dy. We prove the global in-time existence of solutions of IBV problem for nonlinear capillary equation with inhomogeneous Robin boundary conditions. Also we are interested in the study of the asymptotic behavior of solutions.