The dispersion state of each fiber in a yarn plays an important role in the structure-performance relationships of the spun yarn. The limiting dispersion states in the cross-section of the 2 component (P and N) yarn can be represented as the positive wrapped form (PWF), the negative wrapped form (NWF) and the twisted form (TF).In order to evaluate the dispersion state in the spun yarn made of 2 layers of fleeces, the second moment of area is the effective measure. However, the normalized difference between the second moments of each component area, m, depends on the volume fraction of the P-component, u, as well as on the dispersion state. In this paper, an index, μ, which can evaluate the dispersion state independently from the volume fraction, υ, has been proposed and its validity has been confirmed experimentally. In the experiment, the two layered yarns, in which υ varies from 0.35 to 0.65, are spun by the 3 different spinning conditions. It is concluded that the index, , μ, of the spun yarns spun by the same spinning condition has the identical value even if the volume fraction, υ, varies. This result also suggests that the dispersion state is not affected by the doubling process of two fleeces.

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We proposed the strain analysis theory considering radial Young's modulus distribution in yarn package, and theoretical strain distribution is derived by using the data of model experiment which decides radial Young's modulus distribution. The obtained results are as follows :
(1) Strain analysis considering radial Young's modulus distribution come true by separating strain equations and using variable K for the hardness of yarn package.
(2) Effectivness of radial Young's modulus of internal yarn layer is large for strain distribution.
(3) Theoretical strain distribution in yarn package is good agreement to the experimental strain distribution.

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