We report here, for the first time, on spatial oscillations of coronal loops, which were detected in extreme-ultraviolet wavelengths (171 Å) with the Transition Region and Coronal Explorer, in the temperature range of Te~1.0-1.5 MK. The observed loop oscillations occurred during a flare that began at 1998 July 14, 12:55 UT and are most prominent during the first 20 minutes. The oscillating loops connect the penumbra of the leading sunspot to the flare site in the trailing portion. We identified five oscillating loops with an average length of L=130,000+/-30,000 km. The transverse amplitude of the oscillations is A=4100+/-1300 km, and the mean period is T=280+/-30 s. The oscillation mode appears to be a standing wave mode (with fixed nodes at the footpoints). We investigate different MHD wave modes and find that the fast kink mode with a period τ=205(L/1010 cm)(ne/109 cm-3)1/2(B/10 G)-1 s provides the best agreement with the observed period. We propose that the onset of loop oscillations in distant locations is triggered by a signal or disturbance that propagates from the central flare site with a radial speed of ~700 km s-1. Because the observed loop oscillation periods are comparable to photospheric 5 minute oscillations, a resonant coupling between the two systems is possible. We further find evidence for global extreme-UV dimming in the entire active region possibly associated with a coronal mass ejection.