We present results from the first directed search for nontensorial gravitational waves. While general
relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict
waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector,
or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the
first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200
known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper
limits for scalar and vector strains, finding values comparable in magnitude to previously published limits
for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.