The authors consider linear differential equations of the form \[ {dx\over dt}= A(t)x,\tag{1} \] where \(A(t)\) is a linear operator in an arbitrary Banach space. In the case when \(A(t)\) is bounded the authors generalize some well-known results from W. A. Coppel, Massera and Schäffer, Daletskiĭ and Kreĭn and N. van Minh about the roughness of exponential dichotomy of (1). The case when \(A(t)\) is an unbounded operator is considered, too. Sufficient conditions for the roughness of a kind of dichotomy for (1) are derived.