The X-ray spectra of two intermediate type Seyfert galaxies are investigated using ASCA observations separated by more than a year. Both NGC 4388 and ESO 103-G35 exhibit strong, narrow Fe K alpha line emission and absorption by cold neutral gas with a column density ~ 10^23 cm^-2, characteristic of the X-ray spectra of type 2 Seyfert galaxies. The power law continuum flux has changed by a factor of 2 over a time-scale of ~ 2 years for both objects, declining in the case of NGC 4388 and rising in ESO 103-G35. No variation was observed in the equivalent width of the Fe K alpha line in the spectra of NGC 4388, implying that the line flux declined with the continuum. We find that the strength of the line cannot be accounted for by fluorescence in line-of-sight material with the measured column density unless a `leaky-absorber' model of the type favored for IRAS 04575-7537 is employed. The equivalent width of the Fe K alpha emission line is seen to decrease between the observations of ESO 103-G35 while the continuum flux increased. The 1996 observation of ESO 103-G35 can also be fitted with an absorption edge at 7.4 $\pm$ 0.2 keV due to partially ionized iron, and when an ionized absorber model is fitted to the data it is found that the equivalent column of neutral hydrogen rises to 3.5 x 10^23 cm^-2. The Fe K alpha line flux can be accounted by fluorescence in this material alone and this model is also a good representation of the 1988 and 1991 Ginga observations. There is then no requirement for a reflection component in the ASCA spectra of ESO 103-G35 or NGC 4388.

45 pages, 5 tables, 11 figures. Accepted for publication in the Astrophysical Journal