Herein, we properly develop the theory of field-dependent solution NMR shifts in paramagnetic molecules, taking into account both indirect and direct effects. It would also be straightforward to extend the theory developed here to the solid state case. It is possible to formulate the theory using the exact induced field (up to infinite order in the external field). However, this requires numerical integration over all possible orientations of the molecule in solution. An alternative is the expansion of the induced field up to third order in the external field B 0 , which makes it possible to perform the integration over orientations analytically. This corresponds to shifts that are correct up to second order in B 0 . In this context, it turns out that the generalization of Ramsey's τ tensor to paramagnetic molecules can be expressed as a fourth derivative of the Helmholtz free energy. The Van Vleck equation for the susceptibility tensor and the Van den Heuvel-Soncini equation for the chemical shielding tensor are analytical sum-over-states expressions for second derivatives of the Helmholtz free energy. Analogously, in order to calculate the τ tensor, we derive an analytical sumover-states equation for fourth derivatives of the free energy.