The nature of magnetoelectric (ME) interactions has been investigated in lead zirconate titanate (PZT) and (111) or (110) single-crystal nickel zinc ferrites. Data on the dependence of low-frequency ME voltage coefficients on static magnetic field orientation show (i) highest ME coefficients for bias field H along [100] and the smallest for H parallel to [110] and (ii) strongest ME interactions for transverse fields and for samples with Zn concentration of 0.3. Measurements on frequency dependence of ME coefficients reveal resonance enhancement due to bending and radial acoustic modes. The highest voltage coefficient is measured for radial modes in a sample with Zn concentration of 0.2. Theoretical estimates of low-frequency and resonance ME parameters are in very good agreement with data.