Analog neural networks are promising candidates for overcoming the sever energy challenges of digital Neural Network processors. However, noise is an inherent part of analogue circuitry independent if electronic, optical or electro-optical integration is the target. I will discuss fundamental aspects of noise in analogue circuits and will then introduce our analytical framwork describing noise propagation in fully trained deep neural networks comprising nonlinear neurons. Most importantly, we found that noise accumulation can be very efficiently supressed under realistic hardware conditions. As such, neural networks implemented in analog hardware should be very robust to internal noise, which is of fundamental importance for future hardware realizations.