  When scale separation in space and time is poor, the alpha effect and
turbulent diffusivity have to be replaced by integral kernels. Earlier work in
computing these kernels using the test-field method is now generalized to the
case in which both spatial and temporal scale separations are poor. The
approximate form of the kernel is such that it can be treated in a
straightforward manner by solving a partial differential equation for the mean
electromotive force. The resulting mean-field equations are solved for
oscillatory alpha-shear dynamos as well as alpha^2 dynamos in which alpha is
antisymmetric about the equator, making this dynamo also oscillatory. In both
cases, the critical values of the dynamo number is lowered by the fact that the
dynamo is oscillatory.
