  We prove the existence of a straight-field-line coordinate system we call
generalized Boozer coordinates. This coordinate system exists for magnetic
fields with nested toroidal flux surfaces} provided $
\oint\mathrm{d}l/B\:(\mathbf{j}\cdot\nabla\psi)=0$, where symbols have their
usual meaning, and the integral is taken along closed magnetic field lines. All
quasisymmetric fields, regardless of their associated form of equilibria, must
satisfy this condition. This coordinate system presents itself as a convenient
form in which to describe general quasisymmetric configurations and their
properties. Insight can be gained analytically into the difference between
strong and weak forms of quasisymmetry, as well as axisymmetry, and the
interaction of quasisymmetry with different forms of equilibria.
