Sign changes of π (x,q,1) - π(x,q,a)

It is known that under the assumption of the generalized Riemann hypothesis the function π(x,q,1) - π(x,q,a) has infinitely many sign changes. In this article we give an upper bound for the least such sign change. Similarly, assuming the Riemann hypothesis we give a lower bound for the number of sign changes of π(x)-li x. The implied results for the least sign change are weaker than those obtained by numerical methods, however, our method makes no use of computations of zeros of the ζ-function.