ALC-LTL is a temporalized extension of the Description Logic ALC. A program that generates ALC-LTL formulae can be used to test developed applications in the area of temporalized Description Logics(DLs). In this report, we present algorithms and the implementation detail about such a program which randomly generates ALC-axioms and ALC-LTL formulae. The randomness in this program is controlled using a uniformed probability distribution. The program has several parameters which control the generation of ALC-concept descriptions, ALC-axioms and ALC-LTL formulae. For the generation of different formulae, we have recursive algorithms which are accompanied by its termination and soundness proves. The program implement these algorithm using the OWL API which provides a support to access, manipulate and store ALC-concept descriptions, ALC-axioms and ALC-LTLformulae.