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A general class of solutions of the combined electromagnetic and conformally invariant scalar field in a space-time admitting isometries along t, y and z axis is found. An interesting feature of the solutions is that they involve two parameters k1 and k2 which are related to the scalar and electric charges respectively and are such that one can recover from them the vacuum solution, the pure saclar field and the pure electromagnetic field solutions in a straightforward way.

The role of spinning fluid in the presence of an electromagnetic field as a source for the causal Gödel-type metrics has been investigated. It is shown that the spinning fluid with non-zero pressure satisfying the Howking-Ellis strong energy condition can be a reasonable candidate for the causal homogeneaus rotating universe.

It is shown that there cannot be a spherically symmetric cluster of charged particles in stationary equilibrium having the total amount of charge greater than or equal to the total mass. The result has been proved from the regularity conditions in the interior and the conditions of fit at the boundary with the exterior Reissner-Nordström metric. Further a reasonable model is given for a cluster of charged particles representing a conformally flat space-time.

The problem of a conformally invariant scalar field coupled with the gravity has been completely solved in the stationary cylindrically symmetric case. The solutions are such that one can recover from them the Lewis solutions and Levi Civita solutions in a trivial way.