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Let $X$ be the product of two projective spaces and consider the general CICYthreefold $Y$ in $X$ with configuration matrix $A$. We prove the finitenesspart of the analogue of the Clemens' conjecture for such a CICY in lowbidegrees. More precisely, we prove that the number of smooth rational curveson $Y$ with low bidegree and with nondegenerate birational projection is atmost finite (even in cases in which positive dimensional families of degeneraterational curves are known).

Rational curves in CICY's in products of two projective spaces