In order to characterize the complex radiation field produced by heavy-ion beams in water, in particular the lateral dose fall-off and the radiation quality, microdosimetry measurements were performed at GSI Darmstadt using pencil-like beams of 300 MeV/u (12)C and 185 MeV/u (7)Li ions delivered by the heavy-ion synchrotron SIS-18. The ion beams (range in water about 17 cm) were stopped in the center of a 30 x 30 x 30 cm(3) water phantom and their radiation field was investigated by in-phantom measurements using a tissue-equivalent proportional chamber (TEPC). The chamber was placed at 35 different positions in the central plane at various depths along the beam axis and at radial distances of 0, 1, 2, 5 and 10 cm. The off-axis measurements for both (12)C and (7)Li ions show very similar distributions of the lineal energy, all peaking between 1 and 10 keV microm(-1) which is a typical range covered by secondary hydrogen fragments and neutrons. The radiation quality given by the dose-mean lineal energy [Formula in text] was found to be at a constant level of 1-2 keV microm(-1) at radial distances larger than 2 cm. The relative absorbed dose at each position was obtained by integration of the measured spectra normalized to the number of incident primary beam particles. The results confirm that the lateral dose profile of heavy ions shows an extremely steep fall-off, with relative values of about 10(-3), 10(-4) and 10(-5) at the 2, 5 and 10 cm distance from the beam axis, respectively. The depth-dose curves at a fixed distance from the beam axis slowly rise until they reach the depth of the Bragg peak, reflecting the build-up of secondary fragments with increasing penetration depth. The measured (12)C dose profiles were found to be in good agreement with a similar experimental study at HIMAC (Japan).