We provide an example of a strictly subcritical multiclass queueing network which is unstable under the longest job first (LJF) service protocol. It is a reentrant line with two servers and four customer classes. The customer arrivals in our system are modeled by a renewal process with a lattice interarrival time distribution, while the corresponding service times are deterministic. We also present examples of deterministic and stochastic strictly subcritical linear resource sharing networks which are unstable under the LJF policy. Finally, we give an example of a deterministic, strictly subcritical two-node linear network with shared resources which is unstable under the longest remaining time first (LRTF) scheduling algorithm.