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The blazar PKS0537-441 has been observed by Swift between the end of 2004 andNovember 2005. The BAT monitored it recurrently for a total of 2.7 Ms, and theXRT and UVOT pointed it on seven occasions for a total of 67 ks, making it oneof the AGNs best monitored by Swift. The automatic optical and infraredtelescope REM has monitored simultaneously the source at all times. InJanuary-February 2005 PKS0537-441 has been detected at its brightest in opticaland X-rays: more than a factor of 2 brighter in X-rays and about a factor 60brighter in the optical than observed in December 2004. The July 2005observation recorded a fainter X-ray state. The simultaneous optical state,monitored by both Swift UVOT and REM, is high, and in the VRI bands it iscomparable to what was recorded in early January 2005, before the outburst. InNovember 2005, the source subsided both in X-rays and optical to a quiescentstate, having decreased by factors of ~4 and ~60 with respect to theJanuary-February 2005 outburst, respectively. Our monitoring shows an overallwell correlated optical and X-ray decay. On the shorter time scales (days orhours), there is no obvious correlation between X-ray and optical variations,but the former tend to be more pronounced, opposite to what is observed onmonthly time scales. The widely different amplitude of the long termvariability in optical and X-rays is very unusual and makes this observation aunique case study for blazar activity. The spectral energy distributions areinterpreted in terms of the synchrotron and inverse Compton mechanisms within ajet where the plasma radiates via internal shocks and the dissipation dependson the distance of the emitting region from the central engine (abridged).

Simultaneous Swift and REM monitoring of the blazar PKS0537-441 in 2005