We present the results of the first systematic study of correlated var
iability in the X-ray emission and the parsec-scale radio structure of
the ''superluminal'' quasar 3C 345. This quasar is one of a class af
core-dominated flat-spectrum radio sources that are believed to emit X
-rays via the synchrotron self-Compton process. By studying its variab
ility in X-rays, we can test this hypothesis for 3C 345 by modeling th
e expected inverse-Comptom flux from the parsec-scale jet, using param
eters derived from multifrequency VLBI imaging. Since the predicted X-
ray flux is very sensitive to the physical parameters of the compact r
adio-emitting regions, a study of variability, with quasi-simultaneous
X-ray and VLBI data, is of particular interest because it is less sen
sitive to assumptions in the adopted model. The soft X-ray flux densit
y of 3C 345 was observed by the ROSAT PSPC instrument at seven epochs
during 1990-1993, during which time its flux density varied by a facto
r of 2, but with no change in spectral index; The X-ray points closely
track the high-frequency radio Bur light curve. Using a series of VLB
I images, we followed the time evolution of spectral shapes and angula
r sizes of the nucleus and the strongest jet component ''C7,'' at a di
stance of similar or equal to 0.5 mas (2 pc) from the nucleus, and der
ived physical parameters for the components. We find that component C7
, not the nucleus, is the dominant generator of the observed X-rays du
ring 1992-1993. For the nucleus, we applied the inhomogeneous-jet mode
l of Konigl and found find that it underpredicts the X-ray flux for an
y plausible combination of physical parameters derived from observatio
n. A homogeneous sphere, with flux density peaking at a few GHz, is ad
equate for modeling the evolution of C7. This sphere model requires th
at C7 dominated the X-ray emission, unless its Doppler factor is much
greater than 10. This contrasts with the situation at epoch 1990.55, f
or which comparable data (Unwin et al. 1994) showed that the nucleus a
nd C5 (the dominant jet feature at that time) both contributed to the
X-ray emission. We discuss the lack of detectable gamma-rays from 3C 3
45 in relation to other gamma-ray loud blazars with which it shares ma
ny observational properties, Combining the superluminal speed (from VL
BI) and Doppler factor deduced from the synchrotron self-Compton calcu
lation, we solve for the jet kinematics at the position of C7, and we
nd that the jet bends away from the line of sight (from theta similar
or equal to 2 degrees to similar or equal to 10 degrees) and accelerat
es from gamma similar or equal to 5 to greater than or similar to 10 o
ver the range of (deprojected) distance from the nucleus of similar or
equal to 3 to similar or equal to 20 pc.