  The recently completed High Altitude Water Cherenkov (HAWC) gamma-ray
observatory has been taking data with a partial array for more than one year
and is now operating with >95% duty cycle in its full configuration. With an
instantaneous field of view of 2 sr, two-thirds of the sky is surveyed every
day at gamma-ray energies between approximately 100 GeV and 100 TeV. Any source
location in the field of view can be monitored each day, with an exposure of up
to $\sim$ 6 hours. These unprecedented observational capabilities allow us to
continuously scan the highly variable extra-galactic gamma-ray sky. By
monitoring the flaring behavior of Active Galactic Nuclei we aim to
significantly increase the observational data base for characterizing particle
acceleration mechanisms in these sources and for studying cosmological
properties like the extra-galactic background light. In this work we present
first studies of data taken between June 2013 and July 2014 with a partial
array configuration. Flux light curves, binned in week-long intervals, for the
TeV-emitting blazars Markarian 421 and 501 are discussed with respect to
indications of flaring states and we highlight coincident multi-wavelength
observations. Results for both sources show indications of gamma-ray flare
observations and demonstrate that a water Cherenkov detector can monitor
TeV-scale variability of extra-galactic sources on weekly time scales. The
analysis methods presented here can provide daily flux measurements with a
minimum time interval of one transit and will be applied to new data from the
completed HAWC array for monitoring of blazars and other transients.
