In most fishes, you should clip the pelvic fin on the right side (since the left is traditionally used for illustrative purposes). In some species, such as clingfishes, the pelvic fin is modified and diagnostic for the species, so you should clip the right pectoral fin. If the fish lacks pelvic fins and its pectoral fins are small, as is the case for American eel, then clip a small section from the caudal fin. It will heal in short time and won't affect the fish too badly.

I know from experience that in some species, fins grow again after cutting. That happened to me in the case common carp (Cyprinus carpio). After cutting a lobe of the caudal fin, it was completely redone after 3-4 months, and my experiment was compromised (I could not make the difference between fish). Why not use tattoos? It's a less invasive technique, permanent and painless.

Thanks for your answer,

As Daniel says, fins will tend to grow back, so fin clipping should only be viewed only as a short-term marking method. Eel fins can get somewhat ragged, so positively identifying the mark could be tricky. Regardless of whatever marking method you use with eels, you will need to anesthetize the fish (too difficult to handle eels while marking without anesthesia).  Other marking methods used with eels include freeze branding, elastomer injections, and to some extent dye marks). PIT tagging (if you can afford it) is becoming the most popular; long-term mark: relatively rapid, positive individual identification, etc.  Email me if you would like more info/details on marking methods for eels: [email protected].

I used T-bar tags.  Each uniquely numbered.  I recaptured the odd eel (A. dieffenbachii; NZ longfin eel) with missing tag, but most with tag still in place after two years.  Easy to put in without anesthesia.

 Hi Valerie, a colleague uses dye marks, which persist in some cases for many years.