We have developed a new set of transport equations for magnetized, fully ionized gases designed to cover the entire regime from collision-dominated to collisionless flow. The equations are based on a skewed bi-Maxwellian velocity distribution function and describe number density, $n$, flow velocity, ${\vek u}$, parallel and perpendicular temperature, $T_{\parallel}$ and $T_{\perp}$, and heat flow, $\mathbf q$. We choose a velocity distribution function $f(\vek v) = f^{\mathrm{bM}}(1+\phi)$ where $f^{\mathrm{bM}}$ is a bi-Maxwellian and the ‘skewness’, $\phi$, is proportional to $c^3$ instead of the more commonly used $\phi\propto c \ (c \equiv |\vek v-\vek u|)$. We find transport coefficients (heat flux and thermal force) in the collision-dominated limit that are in good agreement with results from classical transport theory. The equations also describe, reasonably well, the flow of collisionless, ionized gases, and should therefore be well suited to describe the transition region–corona–solar wind system and other fully ionized, expanding stellar atmospheres.