  An updated analysis of a targeted search for high-energy neutrinos from
Markarian 421 and Markarian 501 is reported. They are two of the closest and
brightest extragalactic sources in the TeV band. In contrast to other types of
active galactic nuclei, BL Lacs are characterized by rapid and large-amplitude
flux variability. Such radio-loud active galactic nuclei are candidate sources
of the observed high-energy cosmic rays. Because their jet is collimated to our
line of sight, the hadronic interactions with the surrounding medium can
produce an accompanying neutrino and gamma-ray flux. The recent detection of
high-energy neutrinos from the direction of TXS 0506+056 motivates a search for
high-energy neutrinos from blazars with enhanced gamma-ray activity. These two
targeted blazars are subject to long-term monitoring campaigns by the HAWC TeV
gamma-ray observatory located in Mexico. This contribution presents the latest
results of a search and extends previously presented results to a longer period
that covers ANTARES data collected between November 2014 and December 2017. The
gamma-ray light curves of each source were used to search for temporally
correlated neutrinos, potentially produced in hadronic processes.
