  In this article we study immersions of the circle that are tangent to an
Engel structure $\mathcal{D}$. We show that a full $h$-principle does exist as
soon as one excludes the closed orbits of $\mathcal{W}$, the kernel of
$\mathcal{D}$. This is sharp: we elaborate on work of Bryant and Hsu to show
that curves tangent to $\mathcal{W}$ often conform additional isolated
components that cannot be detected at a formal level. We then show that this is
an exceptional phenomenon: if $\mathcal{D}$ is generic, curves tangent to
$\mathcal{W}$ are not isolated anymore.
  We then go on to show that a full $h$-principle holds for immersions
transverse to the Engel structure.
