  Processive molecular motors take more-or-less uniformly sized steps, along
spatially periodic tracks, mostly forwards but increasingly backwards under
loads. Experimentally, the major steps can be resolved clearly within the noise
but one knows biochemically that one or more mechanochemical substeps remain
hidden in each enzymatic cycle. In order to properly interpret experimental
data for back/forward step ratios, mean conditional step-to-step dwell times,
etc., a first-passage analysis has been developed that takes account of hidden
substeps in $N$-state sequential models. The explicit, general results differ
significantly from previous treatments that identify the observed steps with
complete mechanochemical cycles; e.g., the mean dwell times $\tau_+$ and
$\tau_-$ prior to forward and back steps, respectively, are normally {\it
unequal} although the dwell times $\tau_{++}$ and $\tau_{--}$ between {\it
successive} forward and back steps are equal. Illustrative (N=2)-state examples
display a wide range of behavior. The formulation extends to the case of two or
more detectable transitions in a multistate cycle with hidden substeps.
