Before using erythromycin (antibiotic) or any other chemical, please read this:
A little background on the sometimes nasty, but usually benificial "slime". It is one of natures pollution control mechanisms. It is always present as stated by rabagley (post just above this one).
Cyanobacteria (if you are a Zoologist) or blue-green algae (if you are a botanist), (Who's is it? The world may never know), is a prokaryotic (nucleus not bound by membrane) lifeform with chlorophyl. It has charictaristics of both an algae and a bacteria. It can feed like bacteria or it can photosynthesize like an algae.
There are many species of cyanobacteria in both fresh and saltwater, and everywhere inbetween. It can be found in the most unforgiving, inhospitable environments known to science (from the arctic to the boiling hot springs of Yellowstone National Park).
Within the cell walls are contained chlorophyl (green) and one or more of 3 different color pigments, c-phycocyanin (blue), c-allophycocyanin (blue), c-phycoerythrin (red). Your Red slime can appear blue-green at times, or even purple to black depending on what pigmentation is most pridominant at the time.
Some planktonic species can cause serious blooms, and even produce toxins. However, they are necessary for a properly ballanced ecosystem to function.
In the end, is it nasty looking.......yes, but it is a necessary part of the reef's ecosystem. If it gets out of control there is a reason. Get rid of the reason and you get rid of the bloom. If it is a new system It is going to go thru it to one extent or another (just be patient, its the name of the game). Older setups, reduce feeding, and do frequent water changes to get the system back under control. Is another species of algae (say... hair algae) dying off, or a diatom bloom, or dynoflagelate bloom dying off? Cyanobacteria will feed on any decaying organic matter. If you are impatient then consider using Boyd ChemiPure (have good water flow, and follow the instructions on the bottle and it won't hurt your animals) before using an antibiotic. Erythromycin is known to kill nitrifying bacteria and damage the biological filter (if used in high enough concentration to effectively kill the cyanobacteria). But like all antibiotics, bacteria can mutate and become immune to it. They can get used to ChemiClean as well.
Weigh all the possibilities before choosing a solution, and check to see if any of your animals are particularly sensitive to antibiotics.
Just thought people would appreciate "slime algae" more if they knew a little bit more about it.
Good luck.