Hello Tiggy and Schroedel,
Schroedel, from the images you have posted I can say with some confidence that that is indeed dinoflagellates. Tiggy I am less sure about yours. Cyanobacteria as well as dinoflagellates may appear as chains under a microscope.
In both cases however, I would recommend removing as much as possible (sucking it up while siphoning water out of the tank) followed by addition of 1ml of 3% H2O2 per 10 US gal of water. You should look for any adverse reactions exhibited by your corals. Please read my post on page 39 for some reactions I observed after addition of H2O2. As long as these reaction disappear say under an hour it should be fine.
Remember, dinoflagellates dying may release toxins into the water and adversely affect corals and invertebrates.
H2O2 may be more effective in light and there are a few studies using cyanobacteria I believe that show this. I cannot remember the exact papers as I read them quite a while ago. However, as light will promote dinoflagellates reappearing I would keep the tank in dark for 3 days initially.
In short here is what I suggest, remove as much as possible (more than 95%, make sure you leave little to die in the tank) and keep the tank in dark for 3 days. Add 1ml of 3% H2O2 per 10 US gal of water once a day while maintaining the tank in dark. After 3 days the lights may be switched on (I am assuming you have corals) and if the corals have not respond poorly, the dosing should be increased to 1.5ml of 3% H2O2 per 10 US gal of water twice a day about 8 hours apart at least. Keep water ready for a large water change in case of large amounts of dinoflagellates die within the tank.
I hope this is helpful,
Saif