Legendary indicator, developed by legendary trader (B. Williams). Each of its component holds unique and original name. Different indicators setting are not named as periods, but as lips, teeth and jaw of alligator. Behind flamboyant nomeclature, however lays very simple and effective method of trend identification. Alligator forex indicator works amazingly well with oscillators (RSI, CCI, Stochastic) and momentum forex indicators.
Anatomy of Alligator forex indicator

1) JAW (Blue line) calculated as 13- period smoothed moving average
2) Teeth (Red line) calculated as 8- period smoothed moving average
3) Lips (Green line) calculated as 5- period smoothed moving average
Combined power of three moving averages does a good job in distinguishing trend. Once the trend becomes clear we can use other forex indicators or custom technical anaylsis to enter our position.
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Using Alligator forex indicator
Forex trend identification.

Downtrend. Lines alligned from top to bottom: Blue, red, green.

Uptrend. Lines alligned from top to bottom: green, red, blue.
In strong trend three lines of indicators remain clearly separated. When trend begins to reverse green line (lips) will react first and cross red line (teeth). This signal might be used for position exit.

Twisted indicators lines are signalising weak presence of trend (ranging or consolidating market). We should avoid any trading in such circumstances.
According to B.Williams, tangled Alligators lines are synonymous to the beast resting. Longer it rests (lines remain tangled), hungrier it gets for the price and more violent price attack can be expected. After long periods of consolidation substantial moves can be expected.
Placing stop loss.
Alligator forex indicator is used for stop loss placement. Typically, red line is used for that purpose, however it is always necessary to consider market volatility when placing stop loss with alligator forex indicator.