Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback are studied both numerically and experimentally. Mappings of the dynamic states and bifurcation diagrams are compared between a delayed negative optoelectronic feedback system and a delayed positive optoelectronic feedback system. Both systems follow a quasiperiodic route to chaos, where regular pulsing, quasiperiodic pulsing, and chaotic pulsing states are observed. Frequency-locked pulsing states are also found in a delayed negative optoelectronic feedback system, but not in a delayed positive optoelectronic feedback system. These frequency-locked pulsing states are experimentally observed to exhibit a harmonic frequency-locking phenomenon, where the pulsing frequency is locked to a harmonic of the delay loop frequency instead of the delay loop frequency itself. The rotation numbers of these frequency-locked pulsing states show a Devil's staircase structure.