  Thermodynamics in the vicinity of a critical endpoint with nonclassical
exponents $\alpha$, $\beta$, $\gamma$, $\delta$, $...$ is analyzed in terms of
density variables (mole fractions, magnetizations, etc.). The shapes of the
isothermal binodals or two-phase coexistence curves are found at andnear the
endpoint for symmetric and nonsymmetric situations. The spectator- (or
noncritical)-phase binodal at $T=T_{e}$ is characterized by an exponent
$(\delta +1)/\delta$ $(\simeq 1.21)$ with leading corrections of relative order
$1/\delta$ $(\simeq 0.21)$, $\theta_{4}/\beta\delta$ $(\simeq 0.34)$ and $1
-(\beta\delta)^{-1}$$(\simeq 0.36)$; in contrast to classical (van der Waals,
mean field, $...$) theory, the critical endpoint binodal is singular with
leading exponent $(1-\alpha)/\beta$ $(\simeq 2.73)$ and corrections which are
elucidated; the remaining, $\lambda$-line binodals also display the
`renormalized exponent,' $(1-\alpha)/\beta$ butwith more singular corrections.
(The numerical values quoted here pertain to $(d=3)$-dimensional-fluid or
Ising-type systems.)
