We present CCD photometry of SX Phe variables in the field of the globular cluster M 55 .
We have discovered 27 variables , three of which are probable members of the Sagittarius dwarf galaxy .
All of the SX Phe stars in M 55 lie in the blue straggler region of the cluster color-magnitude diagram .
Using period ratio information we have identified the radial pulsation modes for one of the observed variables .
Inspection of the period-luminosity distribution permits the probable identifications of the pulsation modes for most of the rest of the stars in the sample .
We have determined the slope of the period-luminosity relation for SX Phe stars in M 55 pulsating in the fundamental mode .
Using this relation and the HIPPARCOS data for SX Phe itself , we have estimated the apparent distance modulus to M 55 to be ( m - M ) _ { V } = 13.86 \pm 0.25 mag .