  In this paper we derive some new weakly nonlinear asymptotic models
describing viscous waves in deep water with or without surface tension effects.
These asymptotic models take into account several different dissipative effects
and are obtained from the free boundary problems formulated in the works of
Dias, Dyachenko and Zakharov (Physics Letters A, 2008), Jiang, Ting, Perlin and
Schultz (Journal of Fluid Mechanics,1996) and Wu, Liu and Yue (Journal of Fluid
Mechanics, 2006).
