  Let $X_1,X_2,..., X_n,...$ be a stochastic process with independent values
whose distribution $P_\theta$ depends on an unknown parameter $\theta$,
$\theta\in\Theta$, where $\Theta$ is an open subset of the real line. The
problem of testing $H_0:$ $\theta=\theta_0$ vs. a composite alternative $H_1:$
$\theta>\theta_0$ is considered, where $\theta_0\in\Theta$ is a fixed value of
the parameter. The main objective of this work is the characterization of the
structure of the locally most powerful (in the sense of Berk) sequential tests
in this problem.
