J. G. Dai [ibid. 5, No. 1, 49-77 (1995; Zbl 0822.60083)] and J. G. Dai and the author [IEEE Trans. Autom. Control 40, No. 11, 1889-1904 (1995; Zbl 0836.90074)] have demonstrated the stability of the stochastic system via the stability of a fluid approximation. The author establishes a converse result to obtain criteria for transience for stochastic queueing networks based on a fluid limit model. In particular, he shows that if the fluid limit model explodes at a linear rate, then the associated queueing network with independent and identically distributed service times and a renewal arrival process explode faster than any fractional power.