This paper presents the performance analysis of interactive Internet systems, for which the time rate of system offer change is comparable to the users interaction time with the system. In this paper such systems class is called Interactive Internet Systems with Dynamically Changing Offers (IISDCO). In IISDCO systems an offer change may cause cancellation of the started but incomplete transactions. The necessity of cancellation can result from the sale of a set of resources (goods sold) which is getting exhausted or whose price has changed.This paper includes a performance analysis of an on-line stock exchange system (sample of IISDCO). For the analysis we used models in the form of Time Coloured Petri Nets (TCPNs). We also reviewed the proposed models on the example of the Internet on-line stock exchange system.