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We present an experimental investigation of the superconducting transition temperatures, Tc, of superconductor/ferromagnet bilayers with varying the thickness of ferromagnetic layer. FeN was used for the ferromagnetic (F) layer, and NbN and Nb were used for the superconducting (S) layer. The results were obtained using three different-thickness series of the S layer of the S/F bilayers: NbN/FeN with NbN thickness, dNbN ≈ 9.3 nm and dNbN ≈ 10 nm, and Nb/FeN with Nb thickness dNb ≈ 15 nm. Tc drops sharply with increasing thickness of the ferromagnetic layer, dFeN, before maximal suppression of superconductivity at dFeN ≈6.3 nm for dNbN ≈10 nm and at dFeN ≈2.5 nm for dNb ≈ 15 nm, respectively. After shallow minimum of Tc, a weak Tc oscillation was observed in NbN/FeN bilayers, but it was hardly observable in Nb/FeN bilayers.