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We present optical follow-up observations with the DDOTI telescope ofgravitational-wave events detected during the Advanced LIGO and Advanced VirgoO3 observing run. DDOTI is capable of responding to an alert in a few minutes,has an instantaneous field of about 69 deg$^{2}$, and obtains $10\sigma$ upperlimits of $w_{\rm lim}=18.5$ to 20.5 AB mag in 1000~s of exposure, depending onthe conditions. We observed 54\% (26 out of 48) of the unretractedgravitational-wave alerts and did not find any electromagnetic counterparts. Wecompare our upper limits to various possible counterparts: the kilonovaAT~2017gfo, models of radioactive- and magnetar-powered kilonovae, shortgamma-ray burst afterglows, and AGN flares. Although the large positionaluncertainties of GW sources do not allow us to place strong constraints duringO3, DDOTI observations of well-localized GW events in O4 and beyond couldmeaningfully constrain models of compact binary mergers. We show that DDOTI isable to detect kilonovae similar to AT~2017gfo up to about 200~Mpc andmagnetar-powered kilonovae up to 1~Gpc. We calculate that nearby ($\lesssim$200Mpc) afterglows have a high chance ($\approx$70\%) to be detected by rapid($\lesssim$3 hours) DDOTI observations if observed on-axis, whereas off-axisafterglows are unlikely to be seen. Finally, we suggest that long-termmonitoring of massive BBH events with DDOTI could confirm or rule out late AGNflares associated with these events.

DDOTI Observations of Gravitational-Wave Sources Discovered in O3