The main objective of this paper is to present a method of evaluating several tumor markers by using the generalized ROC criterion. This criterion finds the best linear combination of the tumor markers such that the area under the ROC curve is maximized. Confidence intervals for the generalized ROC criteria are also presented. This methodology is applied to 51 patients with advanced colorectal cancer for whom the ACE tumor markers were measured before and during chemotherapy treatment. Two populations were defined according to clinical response to chemotherapy. Each marker taken separately, whether on the raw scale or on the transformed scale, contained 0.5 in the confidence interval and was thus non significant. This was also true for both markers on the raw scale. However, the best linear combination on the logarithms of ACE before and at evaluation gave a significantly better area under the ROC curve. A weighted change in ACE measurements significantly distinguishes between responders and non responders in patients with advanced colorectal cancer. We propose that the methodology presented in this paper be used for the evaluation of several tumor markers.