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We report the results of photometric observations of the blazars Mrk 421 and3C 454.3 designed to search for intraday variability (IDV) and short-termvariability (STV). Optical photometric observations were spread over eighteennights for Mrk 421 and seven nights for 3C 454.3 during our observing run in2009-2010 at the 1.04 m telescope at ARIES, India. Genuine IDV is found for thesource 3C 454.3 but not for Mrk 421. Genuine STV is found for both sources. Mrk421 was revealed by the MAXI X-ray detector on the International Space Stationto be in an exceptionally high flux state in 2010 January - February. Weperformed a correlation between the X-ray and optical bands to search for timedelays and found a weak correlation with higher frequencies leading the lowerfrequencies by about ten days. The blazar 3C 454.3 was found to be in high fluxstate in November-December 2009. We performed correlations in opticalobservations made at three telescopes, along with X-ray data from the MAXIsatellite and public release gamma-ray data from the Fermi space telescope. Wefound strong correlations between the gamma-ray and optical bands at a time lagof about four days but the X-ray flux is not correlated with either. We brieflydiscuss the possible reasons for the time delays between these bands within theframework of existing models for X-ray and gamma-ray emission mechanisms.

Multiwavelength Variability of the Blazars Mrk 421 and 3C 454.3 in the High-State