It is proved that the fugacity coefficient (phi) of a mixture and the fugacity coefficient of component i ((phi) over cap) follow the relation In = [partial derivative(n In (phi) over cap)/partial derivative n(i)](T,P,nj)(j not equal i), = [partial derivative(n In phi)/partial derivative n(i)] where n(i) is the amount-of-substance of component i, and T, P, V-t and n are the temperature, pressure, total volume and total amount-of-substance of the system, respectively. This relation is very useful for. the derivation of (phi) over cap (i). It allows the phi function to contain both P and V, so phi can be expressed with various equations of state (either volume-explicit or pressure-explicit). This approach can also use the similarity of the phi expressions of pure fluids and mixtures to simplify the derivation of (phi) over cap. Besides, (phi) over cap can also be directly derived from equation of state through a variation of the approach above. These approaches are much easier than the commonly used ones when the equation of state for fluids is complex. (C) 2008 Elsevier B.V. All rights reserved.