It is pointed out that a generalized exact relationship exists between the spectroscopic splitting factor

g

and the magnetomechanical ratio

g^{'}

for paramagnetic centers:

g^{'} = \frac{g}{(g - ρ)}

with

ρ = \frac{〈 S_{z} 〉}{{S_{z}}^{'}}

. Here

S^{'}

is the fictitious spin in the spin Hamiltonian and

〈 S_{z} 〉

is the expectation value of the real spin in the state labeled by

{S_{z}}^{'}

; the

z

axis is defined by the direction of magnetic field. Several classes of magnetic systems are considered, where for each system

ρ

is constant over a wide range of physical parameters such as cubic crystal field and spin-orbit coupling, expressing an underlying symmetry of the magnetic ion in its environment. It is shown that the sole criterion for validity of the Kittel-Van Vleck relation

g^{'} = \frac{g}{(g - 1)}

is that

〈 S_{z} 〉 = {S_{z}}^{'}

and that this may occur even when the admixed orbital angular momentum is very large so that the departure of

g

from 2 is very large. The generalized relation between

g

and

g^{'}

is also applied to cases where

g

is negative while

g^{'}

is positive. The extension of the relation between

g

and

g^{'}

to cases of interacting magnetic centers is discussed.

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