lambda-(BETS)(2)GaBrxCl4-(x) [BETS = bis(ethylenedithio)tetraselenafulvalene; 0 less than or equal to x less than or equal to 2] is a molecular superconductor with strongly correlated conduction electrons. The electrical transport properties of lambda(BETS)(2)GaBrx- Cl4-x are drastically changed by varying the bromine content x or by applying pressure. At ambient pressure, the superconducting transition could be observed for x < 0.75. The pressure and x dependencies of T-c were examined. The M-H curve (M = magnetization; H = magnetic field) at 2 K indicated the almost perfect Meissner state of the superconducting phase of lambda-(BETS)(2)CaCl4. The H-cl is similar to 8 Oe for H-perpendicular to and 12 Oe for H-parallel to where H-perpendicular to and H-parallel to are the magnetic fields perpendicular and parallel to the c axis, respectively. The magnetic susceptibility of lambda-(BETS)(2)GaBrxCl4-x increases with decreasing temperature to similar to 60 K, below which the susceptibility becomes x-dependent and tends to be suppressed with increasing x. The isotropic decrease of the static susceptibility at lower temperature observed in the insulating system with x > 1.0 indicates the insulating ground state seems not to be antiferromagnetic but probably nonmagnetic. The crystal structure determinations of a series of lambda-(BETS)(2)GaBrxCl4-x and the calculations of the intermolecular overlap integrals of the highest occupied molecular orbital of BETS were made to elucidate a key factor of the superconducting transition mechanism. The x-dependence of intermolecular overlap integrals seems to suggest that the magnitude of the "spin gap" of the nonmagnetic insulating state tends to be diminished with decreasing x. There exists one intermolecular overlap integral exhibiting a large temperature and x-dependence, which seems to play a crucial role in determining the nature of the ground state.