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The Sparre-Andersen theorem is a remarkable result in one-dimensional random walk theory that states that the probability distribution ρn of the number of steps needed for a walker starting at the origin to land on the positive semi-axes does not depend on the details of the distribution for the jumps of the walker, provided this distribution is symmetric and continuous, where in particular ρn∼ n− 3/2 for large number of steps n. On the other hand, there are many situations in which the time spent by the walker in doing one step depends on the length of the step and the interest concentrates on the time needed for a return, not on the number of steps. Here we modify the Sparre-Andersen proof to deal with such cases, in rather general situations in which the time variable correlates with the step variable. As an example we present a natural process in 2D that shows deviations from normal scaling are present for the first-passage-time-distribution on a semi plane.