To solve the inverse kinematic problem of redundant robot manipulators, two redundancy-resolution schemes are investigated: one is resolved at joint-velocity level, and the other is resolved at joint-acceleration level. Both schemes are reformulated as a quadratic programming (QP) problem. Two recurrent neural networks (RNNs) are then developed for the online solution of the resultant QP problem. The first RNN solver is based on the gradient-descent method and is termed as gradient neural network (GNN). The other solver is based on Zhang 's neural-dynamic method and is termed as Zhang neural network (ZNN). The computer simulations performed on a three-link planar robot arm and the PUMA560 manipulator demonstrate the efficacy of the two redundancy-resolution schemes and two RNN QP-solvers presented, as well as the superiority of the ZNN QP-solver compared to the GNN one. More importantly, the simulation results show that the solutions of the two presented schemes fit well with each other, i.e., the two different-level redundancy-resolution schemes could be equivalent in some sense. The theoretical analysis based on the gradient-descent method and Zhang 's neural-dynamic method further substantiates the new finding about the different-level redundancy-resolution equivalence.