  At the Free-Electron Laser in Hamburg (FLASH) and the European X-Ray
Free-Electron Laser, superconducting TeV-energy superconducting linear
accelerator (TESLA)-type cavities are used for the acceleration of electron
bunches, generating intense free-electron laser (FEL) beams. A long rf pulse
structure allows one to accelerate long bunch trains, which considerably
increases the efficiency of the machine. However, intrabunch-train variations
of rf parameters and misalignments of rf structures induce significant
trajectory variations that may decrease the FEL performance. The accelerating
cavities are housed inside cryomodules, which restricts the ability for direct
alignment measurements. In order to determine the transverse cavity position,
we use a method based on beam-excited dipole modes in the cavities. We have
developed an efficient measurement and signal processing routine and present
its application to multiple accelerating modules at FLASH. The measured rms
cavity offset agrees with the specification of the TESLA modules. For the first
time, the tilt of a TESLA cavity inside a cryomodule is measured. The
preliminary result agrees well with the ratio between the offset and angle
dependence of the dipole mode which we calculated with eigenmode simulations.
