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Considered is the N=1 SQCD-like theory with SU(N_c) colors and 0<N_F<2N_cflavors of light quarks Q_i,\bar Q_j and with the additional N^2_F colorlessflavored fields Phi_{ij} with the large mass parameter \mu_{Phi}>>Lambda. Themass spectra of this Phi-theory (and its dual variant, the dPhi-theory) arecalculated at different values of \mu_{Phi}/Lambda >>1 within the dynamicalscenario which implies the (quasi)spontaneous breaking of chiral symmetry. Itis shown that, under appropriate conditions, the seemingly heavy anddynamically irrelevant fields Phi 'return back' and there appear two additionalgenerations of light Phi-particles with small masses \mu(Phi)<<Lambda.  Also considered is the X-theory which is the N=2 SQCD with SU(N_c) colors and0<N_F<2N_c flavors of light quarks, broken down to N=1 by the large massparameter of the adjoint scalar field X, \mu_X>>Lambda_2. The tightinterrelations between these X and Phi-theories are described, in particular,the conditions under which they are equivalent.

Mass spectra in N=1 SQCD with additional fields. I