Due to the similarity between AFe(2)As(2) (A = Ba, Sr) and RFe(2)Si(2) (R = La, Y and Lu), the RFe(2)Si(2) system has been proposed as a potential candidate for a new high TC superconducting family containing Fe-Si (instead of Fe-As) layers as a structural unit. Various R (Fe(1-x)M(x))2 Si(2) (M = Ni and Cu) materials were synthesized and measured for their magnetic properties. None of these materials is superconducting down to 1.8 K. A pronounced peak at 232 K was observed in the magnetization curve of YFe(2)Si(2). (57)Fe Mössbauer studies confirm the absence of any long-range magnetic ordering below 232 K. Similar peaks at various temperatures also appear in R (Fe(1-x)M(x))2 Si2 samples. For Y (Fe(1-x)Mn(x))2 Si(2) the peak position is dramatically affected by the magnetic Mn dopants. Four independent factors affect the peak position and shift it to lower temperatures: (i) the lattice parameters, (ii) the concentration of x (iii) the applied magnetic field and (iv) the magnetic nature of M. It is proposed that the magnetic peaks observed in RFe(2)Si(2) and in R (Fe(1-x)M(x))2 Si(2) represent a new nearly ferromagnetic Fermi liquid system, its nature is yet to be determined.