New spectra of A78 and A58 at different positions in the nebulae are presented. An abundance gradient is found in A78, extending quite close to the center. Similarly, the nebulous knot near the center of A58 has considerably higher heavy element abundances than the outer regions of this nebula. The ionization state is considerably lower in A58 than A78. In A78 most of the neon is in the form of Ne(3+) and Ne(4+), indicating that the standard ionization correction factor as used by Jacoby and Ford (1983), is substantially in error. Finally, the very high infrared excesses found in these nebulae are discussed.