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The objective of the Taiwan Research Reactor project is to modify the Taiwan Research Reactor (TRR) into a multi-purpose medium-flux research reactor (TRR-II). The project started in 1998, and the estimated maximum unperturbed thermal neutron flux (E < 0.625 eV) of the new reactor is approximately 2.7 × 10[sup 14] n/cm² s. The major application areas of TRR-II are: neutron scattering in material and biological researches, material tests, neutron-activation analyses, isotope production and industrial applications. The new TRR-II reactor will have five thermal neutron beam tubes (BT2-6) and a cold-neutron source with two extended cold-neutron beam tubes (BT1 and BT8) to install a maximum of 16 neutron scattering/absorption instruments. Four primary neutron guides will be installed inside BT8 to guide cold neutrons to the guide hall, and four spectrometers are planned in this project. The four planned spectrometers are: a 40-m small-angle neutron-scattering (SANS) instrument, a high-resolution powder diffractometer (HRPD), a vertical focusing reflectometer (RF) and a triple-axis spectrometer (TAS). The SANS and RF will be installed at the guide hall using cold neutrons, and the HRPD and TAS will be installed at the reactor building using thermal neutrons. This paper describes the conceptual design of the four planned spectrometers of the TRR-II project. [ABSTRACT FROM AUTHOR]