  The paper studies the local solvability and subellipticity for square systems
of principal type. These are the systems for which the principal symbol
vanishes of first order on its kernel. For systems of principal type having
constant characteristics, local solvability is equivalent to condition (PSI) on
the eigenvalues, see arXiv:0801.4043. This is a condition on the sign changes
of the imaginary part of the eigenvalue along the oriented bicharacteristics of
the real part.
  In the generic case when the principal symbol does not have constant
characteristics, condition (PSI) is not sufficient, not invariant and in
general not well defined. Instead we study systems which are
quasi-symmetrizable, these systems have natural invariance properties and are
of principal type. We prove that quasi-symmetrizable systems are locally
solvable. We also study the subellipticity of quasi-symmetrizable systems in
the case when principal symbol vanishes of finite order along the
bicharacteristics. In order to prove subellipticity, we assume that the
principal symbol has the approximation property, which implies that there are
no transversal bicharacteristics.
