The fetal electrocardiogram (fECG) contains important information regarding the health of the fetus. However, the fECG obtained noninvasively from the abdominal surface electrical recordings of a pregnant woman are dominated by strong interference from the maternal electrocardiogram (mECG). In this paper, based on the H(infinity) principle, two adaptive algorithms are proposed for the extraction of fECG from the trans-abdominal recordings of pregnant women. The motivation behind the application of H(infinity) techniques is the fact that they are robust with respect to model uncertainties and lack of statistical information regarding noise. The proposed algorithms are applied to simulated as well as real multichannel ECG recordings and their performances are compared to that of the well-known least-mean-square (LMS) adaptive algorithm. It is found that the proposed H(infinity) based algorithms perform superior to the LMS algorithm in extracting the fECG signal.