  We introduce rigid syntomic cohomology for strictly semistable log schemes
over a complete discrete valuation ring of mixed characteristic (0,p). In case
a good compactification exists, we compare this cohomology theory to
Nekov\'a\v{r}-Nizio{\l}'s crystalline syntomic cohomology of the generic fibre.
The main ingredients are a modification of Gro{\ss}e-Kl\"onne's rigid
Hyodo-Kato theory and a generalisation of it for strictly semistable log
schemes with boundary.
