The same approach used by the authors in the context of advancing and receding contact lines is applied to the case of liquid-liquid contact lines. The result is an ordinary differential equation whose solution provides an approximate description of the shape of a moving meniscus. It is shown that a system with a viscosity ratio of 10(3) or more may be regarded as being a purely advancing/receding case. From the comparison of the present model with experimental results a dependence of the true contact angle on the line speed is inferred.