This paper deals with the adaptive blind source separation problem in presence of impulsive noise. New algorithms extending the well known SOBI method from batch to adaptive scheme are introduced. At first, the standard Gaussian noise case is considered, leading to our first algorithm referred to as Adaptive SOBI (A-SOBI). Later on, a robust version of A-SOBI, referred to as RA-SOBI is derived to handle the impulsive noise case. RA-SOBI relies on robust subspace tracking for the whitening stage together with robust correlation estimation for the separation stage. All proposed algorithms are of relatively low complexity and allow to achieve good separation quality as illustrated by our simulation results.