Self-diffusion and relaxation time studies of C3 to C6 hydrocarbons adsorbed in the microporous metal−organic framework CuBTC were performed by nuclear magnetic resonance (NMR) in the temperature range of 193−373 K. The presence of paramagnetic copper species in the solid CuBTC framework leads to short longitudinal (T1) and transverse (T2) relaxation times of the hydrocarbons with typical values of T1 ≲ 10 ms and T2 ≲ 3 ms. Under these conditions, pulsed field gradient (PFG) NMR self-diffusion studies could only be performed at short observation times using the primary spin echo sequence with high-intensity pulsed magnetic field gradients. The obtained temperature dependent self-diffusion coefficients were analyzed using an Arrhenius approach. The activation energies of the alkanes are in the range of 6.5−8.5 kJ/mol, increasing slightly with increasing number of carbon atoms. Significantly higher values were found for propene (13.2 kJ/mol) and 1-butene (15.0 kJ/mol). These tendencies are consistent with corresponding measurements of heats of adsorption and with data obtained in molecular dynamics (MD) simulations. The MD simulations show a strong dependence of the heat of adsorption and diffusion on loading and temperature. This is caused by the preferential adsorption of small alkanes such as propane and butane in the side pockets of the CuBTC structure at low loading and temperature.