The paper proposes a class of compressive distributed adaptive filtering algorithms, aiming to estimate unknown high-dimensional and sparse parameters in sensor networks, based on compressive sensing (CS) method. The algorithms first use compression estimation to obtain the compressed unknown parameters, then apply decompression algorithms to obtain the desired estimates. In the paper, we focus on compressive distributed least mean square (CDLMS) algorithms and show that the algorithms can fulfil the estimation or tracking tasks under a compressed information condition, which is weaker than the information condition for distributed LMS algorithm in [1].