The main aim of this thesis is to investigate non-Einsteinian interactions in a scalartensor theory and a tensor-tensor theory of gravity with torsion. We first explore perfect fluid and spinning particle dynamics in a scalar-tensor theory of gravity with scalar field interactions, and derive equations of motion for a charged perfect fluid both from gauge identities and a variational principle in background nonRiemannian spacetime (metric compatible connection with torsion), a scalar field and an electrom(l.gnetic field. For a spinning particle, we use gauge identities with given source currents to obtain its equations of motion with scalar field interactions, and solve its equations of motion in two different backgrounds: one is a BransDicke torsion field and the other is a constant pseudo-Riemannian curvature with constant scalar field and zero torsion. Moreover, we calculate the precession of a gyroscope moving along abound orbit in the weak limit of a vacuum Kerr-BransDicke solution with torsion. In Chapter 4, the equations of motion for massive spinless particles in a tensor-tensor theory of gravity with torsion are investigated. We first apply the perturbation scheme to the system of field equations and discover a perturbed torsion wave solution. Furthermore, we obtain gauge transformations of perturbed field variables and examine the polarizations of this torsion wave solution from autoparallel deviation. The longitudinal modes of the torsion wave polarization has been found. The polarizations (both transverse and longitudinal modes) of the torsion wave are quite different from the gravitational wave in the linearized GR.