Let $X^{\dagger}\rightarrow S^{\dagger}$ be a morphism of fine saturated log schemes. A log curve in $X^{\dagger}$ with base $W^{\dagger}$ is a log curve $C^{\dagger}/W^{\dagger}$ together with a morphism $f:C^{\dagger}\rightarrow X^{\dagger}$ fitting into a commutative diagram of log schemes

A log curve in $X^{\dagger}$ is a stable log map if for every geometric point $\bar{w}\rightarrow W$, the restriction of $f$ to the underlying marked curve $C_{\bar{w}}\rightarrow\bar{w}$ is an ordinary stable map. We write the data as $(C^{\dagger}/W^{\dagger},f)$.

This definition can be further decorated in the usual way by labelling marked points.