We analyze the transmission of many wavelength-division-multiplexed (WDM) channels through a cascade of Erbium-doped fiber amplifiers (EDFA) in both long-distance links and ring-based networks. For a megameter long-distance system, optimal operating conditions are found for achieving a high signal-to-noise ratio (SNR) per channel with as small an SNR differential as possible between 20 WDM channels spaced 0.5 nm apart. Critical issues addressed in this paper include: 1) the non-uniformity of the EDFA gain with wavelength; 2) the link loss between amplifiers; (c) the small-signal gain per amplifier; and (d) the input signal power. We find that the link loss is the most critical parameter for narrowing the SNR differential between the 20 channels, and that a 25-dB small-signal gain for each amplifier provides the highest overall SNR for the 20 channels transmitted across 4500 km. Additionally, through the incorporation of optical filters in a cascade of EDFA's, we determine the optimal conditions for passively equalizing many WDM channels while maintaining a high SNR for all channels. It is found that if a notch filter, having a 3-dB bandwidth of 2 nm and a center wavelength of 1560 nm, is placed after every group of 20 EDFA's, then an equalized SNR performance for potential megameter transmission is realized. This performance is achieved with no a priori knowledge of the input or output signals. As an extension of cascaded EDFA's, we have also analyzed the critical parameters in an optically amplified WDM ring network which represents an infinite cascade of amplifiers in a closed loop. We find that a ring can accommodate 25 nodes when incorporating an EDFA and a channel-dropping filter in each node, a significant advance over non-amplified rings. We compare several node configurations, and find that the sequence of an EDFA followed by an optical tap and then a channel dropping filter provides the best performance for a wide range in system variables including input signal power, inter-node link loss and its variability, power-tapping ratio, and small-signal gain. The relative insensitivity to the variability in link loss allows for the realization of limited modular expansion of the network.