Abstract <p> One of the constructions for obtaining flows on a manifold is the construction of a suspension over a diffeomorphism. S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. The converse is not true in the general case. A classic illustration of this fact are examples of nonconjugate diffeomorphisms of a circle whose suspensions are equivalent. In this paper, we establish relations between the invariants of topological conjugacy of Cartesian products of rough transformations of a circle and the invariants of topological equivalence of suspensions over them. </p> <p> <b> DOI</b> 10.1134/S1061920824601794 </p>