Abstract: In this talk, we study some control problems related to steering of dynamics of coupled spins in Nuclear Magnetic Resonance (NMR) spectroscopy. These problems arise in transfer of coherence between coupled spins in high resolution two-dimensional NMR experiments. Synthesizing a Unitary transformation on coupled spin systems in minimum time can help reduce relaxation losses and improve signal to noise ratio in NMR experiments. We show how reachable sets for these time optimal control problems evolving on compact Lie groups can be analytically characterized.