Lateral degrees of freedom in resonant tunneling heterostructure devices are investigated in a model which omits the usual assumption that the electric field and current density are laterally uniform. Relaxation of spatially nonuniform configurations of field and current into the usual uniform configurations is examined. For certain device parameters and operating conditions, stable nonuniform configurations are found in addition to the conventional uniform configurations. An eigenvalue criterion for stability is established. The possibility of nonuniform configurations with spatially localized oscillation is also discussed.