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 bound-
ary 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 ).