Single-reference and multi-reference noise canceller (SRNC and MRNC) performances are investigated based on correlation between signal and noise. Exact relations between these noise canceller performances and signal-noise correlation have not been well discussed yet. In this paper, the above relations are investigated based on theoretical, analysis and computer simulation. The normalized LMS (NLMS) algorithm is employed. Uncorrelate, partially correlated, and correlated signal and noise combinations are taken into account. Computer simulation is carried out, using real speech, white noise, real noise sound, sine wave signals, and their combinations. In the SRNC problem, spectral analysis is applied to derive the canceller output power spectrum. From the simulation results, it is proven that the SRNC performance is inversely proportional to the signal-noise correlation as expected by the theoretical analysis. From the simulation results, the MRNC performance is more sensitive to the signal-noise correlation than that of SRNC. When the signal-noise correlation is high, by using a larger number of adaptive filter taps, the noise is reduced more, and, the signal distortion is increased. This means the signal components included in the noise are canceled exactly.