gdodd;
The term HSLA is very broad indeed, and has to be used with care. There are older versions of HSLA steels (like USS T1, HY80, HY100, etc) and you have the newer versions of HSLA steels (microalloy). The more common HSLA steels have been separated out into various classes or forms - weathering steels, microalloyed ferrite/pearlite steels, as-rolled pearlitic steels, low-carbon bainitic steels, dual phase (as you mentioned) steels and inclusion shape controlled steels.
The required strength levels for these steels can be obtained thru specific heat treatments like quench/temper and thru microalloying additions (vanadium,titanium, niobium, nitrogen, copper). The microalloyed HSLA steels during fabrication result in fine grained (enhanced toughness) structures with increasing yield strength obtained thru precipitation strengthening.
As with any welding operation, heat will alter grain size and the distribution/location of phases and preciptates within the HSLA steel microstructure, thus affecting desired properties. Keeping the heat input prior to (preheat temperature) and during welding (interpass temperature) to the minimum recommended by the steel manufacturer is the key to maintaining a localized heat affected zone.