  We prove that all star vector fields, including Lorenz attractors and
multisingular hyperbolic vector fields, admit the intermediate entropy
property. To be precise, if $X$ is a star vector field with $h_{top}(X)>0$,
then for any $h\in [0,h_{top}(X))$, there exists an ergodic invariant measure
$\mu$ of $X$ such that $h_{\mu}(X)=h$. Moreover, we show that the topological
entropy is lower semi-continuous for star vector fields.

Dynamical Systems