A molecular theory for the reptational dynamics of rods with a small p
ersistent flexibility in the liquid crystalline state is developed. A
closed diffusion equation for the orientational distribution function
is obtained by expanding in the small parameter L/l, where L is the co
ntour length of the rodlike polymer chain and l is the persistence len
gth. The Leslie viscosities alpha3 and alpha2 are calculated, and it i
s found that the ratio alpha3/alpha2 is nonmonotonic with L/l. It is c
oncluded that slightly flexible rodlike polymers are more prone to tum
bling nematics than fully rigid rods.