  Inclusive $K^+$ and exclusive $K^+Y$ photoproduction on the deuteron are
investigated theoretically. Modern hyperon-nucleon forces and a recently
updated kaon photoproduction operator for the $\gamma +N\to K^++Y$ process are
used. Sizable effects of the hyperon-nucleon final state interaction are found
near the $K^+\Lambda N$ and $K^+\Sigma N$ thresholds in the inclusive reaction.
Angular distributions for the exclusive process show clear $YN$ final state
interaction effects in certain kinematic regions. Precise data especially for
the inclusive process around the $K^+\Sigma N$ threshold would help to clarify
the strength and property of the $\Lambda N-\Sigma N$ interaction.
