The crossover behavior of the susceptibilities ${\ensuremath{\chi}}^{\ensuremath{\alpha}\ensuremath{\alpha}}$ of spin systems with anisotropic exchange coupling is discussed on the basis of an "extended" scaling hypothesis which gives ${\ensuremath{\chi}}^{\ensuremath{\alpha}\ensuremath{\alpha}}(T,g)\ensuremath{\approx}A{t}^{\ensuremath{-}\ensuremath{\gamma}}{X}_{\ensuremath{\alpha}}(\frac{Bg}{{t}^{\ensuremath{\varphi}}})$, where
g is the anisotropy parameter, $t=\frac{(T\ensuremath{-}{T}_{c0})}{{T}_{c0}}$, with
Tc0 and $\ensuremath{\gamma}$ being the iso tropic critical temperature, and susceptibility exponent, while
A and
B are model-dependent amplitudes. Analysis of high-temperature series expansions for ${\ensuremath{\chi}}^{\ensuremath{\alpha}\ensuremath{\alpha}}(T,g)$ as polynomials in
g for rhombic and axial anisotropy in the fcc, bcc, and simple cubic classical Heisenberg (
n=3) and classical
XY and planar-spin models (
N=2), verifies the scaling with crossover exponents $\ensuremath{\varphi}=1.25\ifmmode\pm\else\textpm\fi{}0.015$ (
n=3) and $\ensuremath{\varphi}=1.175\ifmmode\pm\else\textpm\fi{}0.015$ (
n=2). The universality of the scaling functions ${X}_{\ensuremath{\alpha}}(x)$ is demonstrated both for small
x and in the anisotropic limit $T\ensuremath{\rightarrow}{T}_{c}(g)$, where $x\ensuremath{\rightarrow}\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{x}$; for
n=3, accurate representations are constructed in the form ${X}_{\ensuremath{\alpha}}(x)\ensuremath{\simeq}{P}_{\ensuremath{\alpha}}(\frac{x}{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{x}}){(1\ensuremath{-}\frac{x}{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{x}})}^{\ensuremath{-}\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}$, where $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ is the anisotropic susceptibility exponent, while ${P}_{\ensuremath{\alpha}}(z)$ varies smoothly from ${P}_{\ensuremath{\alpha}}(0)=1$ to ${P}_{\ensuremath{\alpha}}(1)\ensuremath{\simeq}1.10$.