The article extends the Libor market model to include general semimartingales. Special simplifications are found for certain types of semimartingales, like when forward Libor rates are driven by a Brownian motion and a random measure. The drift of the forward Libor system is determined based on the covariation matrix and Levy measure of the system. The study establishes necessary and sufficient conditions and provides formulae for forward Libor rates and bond prices in different measures. It also discusses topics like continuous compounding and model construction.