  New CCD photometry has been combined with published and unpublished earlier
observations to study the three Cepheid variables in M13: V1, V2 and V6. The
light curve characteristics in $B$, $V$ and $I_{\rm C}$ have been determined
and the periods updated. A period change analysis shows all three stars have
increasing periods but for V1 and V2 the rate of period increase does not
appear to be constant over the 118 years of observation. The observed rates of
period increase are in good agreement with the predictions of the Pisa
theoretical models with helium abundance $Y = 0.25$. Theory suggests V1 and V6
have masses of $\sim0.57\,M_\odot$ and are in the redward-evolving final stage
of the ``blue loop'' evolutionary phase that is produced when helium-shell
ignition occurs. The larger period and period change rate for V2 indicate it
has a mass of $\sim0.52\,M_\odot$. A study of eighteen metal-poor BL Her stars
shows the observed period changes for such objects in general can be reasonably
well explained using the predictions from horizontal branch evolutionary
tracks. BL Her stars with periods less than $\sim$3 d and relatively large
secular period change rates ($dP/dt\approx5-15$ d/Myr) are in the evolutionary
stage before He-shell ignition; the remaining cases are stars that have already
experienced He-shell ignition. Moreover, an analysis of crossing time through
the instability strip indicates that it is likely that few, if any, BL Her
stars have a He abundance as large as $Y = 0.33$.

Solar and Stellar Astrophysics