I installed the Arduino IDE according to the arduino.cc instructions (invoking install.sh) rather than sudo apt install .... It is also necessary to have added myself as a user to the group dialout. The ports /dev/ttyACM* were present but I could not download a program to the Adafruit Feather 32u4. I deleted the IDE and reinstalled and the ports disappeared.

I have applied this fix for using the Arduino IDE on Linux which involves placing this file:

99-adafruit-boards.rules into the directory /etc/udev/rules.d/

and rebooting.

According to this page on Arduino for Linux there ought to be some devices at /dev/ttyACM* but mine are missing. What is the solution to this problem? I have replaced the USB cable and it makes no difference.

Edit: The board is Adafruit Feather 32u4 which has an ATmega32u4. The OS is Ubuntu 16.04.