The Ba x Sr 1−x TiO 3 ferroelectric ceramics with magnesium (BSM) and neodymium (BSN) additives were studied. Measurements were made of tunability, dielectric losses (tan δ), leakage currents, the correlations between current-voltage I (U ) and capacitance-voltage C(U ) characteristics. I (U ) characteristics of high quality BSM ceramics have four regions: Ohmic, where the conductivity is linear; the horizontal region (or negative differential resistivity); the exponential dependence; and the vertical current enhancement. These BSM samples (∼20% Mg additives) were distinguished by highest breakdown strength (more than 1000 V), low tan δ (less than 10 −3 at 1 MHz) and high tunability (up to 10% at E max ∼2 V/μm).