In the original paper, Fossen and Grovlen (ibid., vol.6, p.121-8, 1998) proposed the use of an observer-based backstepping method for the dynamic positioning of ships. This note points out that the observer design used does not cover unstable ship dynamics and suggests a remedy for an extended class of ships. The proof for the nonlinear observer used in the design in the above-mentioned papers only applies to ships with stable sway-yaw dynamics. An example concerning thruster assisted mooring of a tanker is considered. It does not fulfil the needed stability properties, so an extension to this case is highly motivated. We propose a method to extend the results, under a detectability condition. This condition implies stable surge dynamics, which is a natural assumption for ships.