Au(110) and Pt(110), which both are (1 x 2) MR (missing-row) reconstructed at 300 K, are well known to undergo two phase transitions upon heating: an Ising transition, in which the surfaces deconstruct, and a 3D roughening transition. Our real-space investigation, with atomic-scale resolution by high-temperature scanning tunneling microscopy, reveals that Pt (110)(1 x 2) deconstructs via the formation of 2D island/hole units in accordance with theory. The MR configuration of Au(110) - in contrast to the present theoretical models - is stable close to the roughening temperature. The order-disorder transition seems to be due to the 2D roughening of already-existing step edges. In view of recent findings of tip-assisted movement of single atoms already at moderate tunneling conditions, e.g. on Ag(110), we discuss and eventually exclude the influence of tip/surface interactions on the relevant structural transformations of the two surfaces. (C) 2000 Elsevier Science B.V. All rights reserved.