We present TESTOR, a tool for on-the-fly conformance test case generation, guided by test purposes. Concretely, given a formal specification of a system and a test purpose, TESTOR automatically generates test cases, which assess using black box testing techniques the conformance to the specification of a system under test. In this context, a test purpose describes the goal states to be reached by the test and enables one to indicate parts of the specification that should be ignored during the testing process. Compared to the existing tool TGV, TESTOR has a more modular architecture, based on generic graph transformation components , is capable of extracting a test case completely on the fly, and enables a more flexible expression of test purposes, taking advantage of the multiway rendezvous. TESTOR has been implemented on top of the CADP verification toolbox, evaluated on three published case-studies and more than 10000 examples taken from the non-regression test suites of CADP.