Photoneutron (PN) dosimetry in fast, epithermal and thermal energy ranges originated from the beam and albedo neutrons in high-energy X-ray medical accelerators is highly important from scientific, technical, radiation protection and medical physics points of view. Detailed dose equivalents in the fast, epithermal and thermal PN energy ranges in air up to 2m as well as at 35 positions from the central axis of 12 cross sections of the phantom at different depths were determined in 18MV X-ray beams of a Siemens ONCOR accelerator. A novel dosimetry method based on polycarbonate track dosimeters (PCTD)/10B (with/without cadmium cover) was used to determine and separate different PN dose equivalents in air and in a multilayer polyethylene phantom. Dose equivalent distributions of PNs, as originated from the main beam and/or albedo PNs, on cross-plane, in-plane and diagonal axes in 10cm×10cm fields are reported. PN dose equivalent distributions on the 3 axes have their maxima at the isocenter. Epithermal and thermal PN depth dose equivalent distributions in the phantom for different positions studied peak at ∼3cm depth. The neutron dosimeters used for the first time in such studies are highly effective for separating dose equivalents of PNs in the studied energy ranges (beam and/or albedo). The PN dose equivalent data matrix made available in this paper is highly essential for detailed patient dosimetry in general and for estimating secondary cancer risks in particular.