An on-line scheme for identifying stable or unstable linear time-invariant processes subject to a class of deterministic and/or stochastic disturbances is proposed. The disturbances are restricted to be the outputs of some unknown linear time-invariant system. The identification scheme consists of: (a) a probing signal input which is a sum of sinusoids (or an exponentially increasing sum of sinusoids when the process is unstable or the disturbances are unbounded), (6) linear time-varying filters which have the properties of asymptotic stability, asymptotic signal tracking and asymptotic noise annihilation, and (c) a parameter update algorithm which uses the filtered input-output data. The frequency response of the process (at the probing signal frequencies) is also estimated. The proposed scheme is verified by simulation.