Recently six conjectures on linear complexities (LC) of some Kronecker sequences of two or three component sequences are proposed by Karkkainen. In, the LC of Kronecker sequences of two component sequences were studied by Uehara and Imamura, their results are true except in the case when eb 2 or when ea = eb = 1. In this paper the LC for Kronecker sequences of two component sequences are determined completely, and it is shown that all the six conjectures are true except in some special cases, which are listed and corrected.