It is well established that many life forms, lower as well as higher, are capable of sensing electromagnetic fields and to use them in order to sustain their survival. Some of them, such as electric rays, utilise this feature to locate pray and display the capability to detect electric fields as low as 0.1 mV/m generated by normal bodily functions of pray fish. Epidemiological research indicates that the alternating magnetic fields within mT range can be a health risk factor. The results of numerous experimental investigations suggest that in a variety of biological systems, including humans, the electromagnetic fields may interfere with the functioning of cells through the calcium signalling pathways. Because of the electromagnetic properties of biological tissue, some of the most probable molecular sites for the field coupling with these pathways are ion channels located within various cellular membranes. In this study the interaction of low-frequency weak electromagnetic signals with ion channels and their effects on intracellular Ca2+ intracellular oscillations in human leukemic T cell line Jurkat have been investigated theoretically, by numerical simulations, and experimentally with the help of microfluorimetry and digital imaging. In T lymphocytes, similarly to many other types of a cell, an external stimulation may lead to oscillatory changes of intracellular Ca2+ concentration. It is generally accepted that both the oscillation frequency and amplitude may be involved in the transduction of the external signal to some intracellular target. In this study it is shown that poly-L-lysine, a highly positively charged peptide widely used to enhance the attachment of cells to supporting surface, under certain conditions forces Jurkat T cells into a state of sustained intracellular Ca2+ spiking for up to 3 hours. Such cells represent the cytosolic calcium oscillator, and they are used in this study to investigate the effects of 50 Hz alternating magnetic fields on calcium signalling in cells. Microfluorimetric recording of intracellular Ca2+ in oscillating cells demonstrated that the total spectral power of the cytosolic Ca2+ oscillator was reduced by exposure of the cells to an alternating magnetic field and that the effect increased in an explicit dose response manner. Many biochemical processes and subcellular components are involved in sustaining the oscillatory behaviour of intracellular Ca2+. The precise mechanisms and components involved in mediating the field effects on oscillation magnitude remain elusive. One of the main problems in understanding the biological effects of the low-frequency weak electromagnetic fields is the low energy of the perturbations inflicted on subcellular components by these fields. The amplification of primary signals within cells is necessary prior to inducement of any biological response. It is shown in this study theoretically and by numerical simulations that such amplification can be achieved by a system of identical ion channels embedded in a cell membrane. The amplification of the signal amplitude relative to the noise amplitude is found to be proportional to the square root of the number of channels modulated and inversely proportional to the square root of the sum of the channel dwell times. Further, the possibility that the cytosolic calcium oscillator is the subcellular system that responds to this amplified signal is explored. Using mathematical models of intracellular Ca2+ oscillations, it is shown by numerical simulations of the non-linear system of differential equations that the cytosolic calcium oscillator is a sensitive detector of external influencies. Its response to the external forcing signal exhibits a multitude of frequency and amplitude "windows". It also exhibits resonance behaviour. From these results it is concluded that forcing of the cytosolic calcium oscillator by external alternating magnetic and electric fields amplified by mechanisms available to cells may be one of the mechanisms of field interaction with biological systems