The CFD modeling of two dimensional multiphase ows is a useful tool in industry, although accurate modeling itself remains a difficult task. One of the difficulties is to track the complicated topological deformations of the interfaces between di erent phases. This paper describes a marker-particle method designed to track fluid interfaces for fluid ows of at least three phases. The interface-tracking scheme presented in this paper is the first part of a series of papers presenting our complete model based on a one-field Godunov marker-particle projection scheme (GMPPS). In this part, we shall focus on the presentation of the interface-tracking scheme and the kinematic tests we conducted to examine the scheme's ability to accurately track interfacial movements typified by vorticity-induced stretching and tearing of the interface. Our test results show that for a set of carefully-designed and commonly-used error measures, relative percentage errors never exceed two percent for all of the tests and grid sizes considered, provided a sufficient number of marker particles are used. We shall also demonstrate that the method is of second order accuracy and the interface transition width remains constant never exceeding three cell widths.