This Licentiate thesis is divided into three parts corresponding to three different papers. There is one research report, one conference paper and one submitted journal paper. All three parts deal with acoustic echo and/or noise cancelling problems when using adaptive microphone arrays. In particular, the papers address the performance of an adaptive microphone array in a small enclosure such as the car cabin. A calibrating scheme is proposed which is independent of array geometry and channel matching, and which calibrates the adaptive array to the given acoustic environment and to the given electronic equipment. Results from real measurements in a car interior are included and compared with an analytical description of an adaptive microphone array. Part A gives an analytical description of an adaptive microphone array which facilitates a simple built-in calibration to the environment and instrumentation. Part B describes the method for performing acoustic echo cancelling with a dig-ital "on-site", "self-calibrating" microphone array system. The calibration process is a simple indirect calibration which continuously adapts to the actual environment and electronic equipment. There is a US patent based on this part and an international patent is currently under examination. Part C presents a neural network based microphone array system, which is capable to continuously perform speech enhancement and adaptation to nonuniform quantization, such as A-law and µ-law.