Because of the rapid progress of DSP hardware performance, the application of active noise control to a moving noise source has become a much more realistic problem. This study describes the preliminary investigations concerning the behavior of a multichannel adaptive algorithm with a moving primary source. The steepest descent algorithms, such as multiple error filtered-x LMS, are often used in practical feedforward active control applications. A previous study showed that the stability and the performance of this algorithm strongly depend on the estimation errors of the transfer responses of the acoustic plant being controlled. The effect of the primary signal variations including the Doppler effect, however, had hardly been investigated. In this study, the convergence properties of the algorithms with the moving sound source were examined by numerical simulations. To simplify the problems and clarify the substantial limitations of the system, a pure tone and a simple free field was assumed as the primary signal and the sound field, respectively. Results showed that the system could converge, and the possible attenuation was varied corresponding to the positions of the primary source.