  The reactions $pp\to p\Lambda K^+$ and $pp\to p\Sigma^0K^+$ are studied near
their thresholds. The strangeness production process is described by the $\pi$-
and $K$ exchange mechanisms. Effects from the final state interaction in the
hyperon-nucleon system are taken into account rigorously. It is found that the
$\Lambda$ production is dominated by $K$ exchange whereas $K$- as well as $\pi$
exchange play an important role for the $\Sigma^0$ case. It is shown that the
experimentally observed strong suppression of $\Sigma^0$ production compared to
$\Lambda$ production at the same excess energy can be explained by a
destructive interference between $\pi$ and $K$ exchange in the reaction $pp\to
p\Sigma^0K^+$. Implications of such an interference on the reaction $pp\to
n\Sigma^+K^+$ are pointed out.
