The invention relates to novel cosmetic compositions comprising: (i) -one or more non-volatile, non-amino polydimethylsiloxanes, (ii) -one or more acyclic liquid fatty esters of a monoalcohol, and (iii) -one or more amino silicones different from the polysiloxanes (i) and chosen from the compounds corresponding to formula (I) below: (R1)a(T)3-a-Si[OSi(T)2]n-[OSi(T)b(R1)2-b]m-OSi(T)3-a-(R1)a The compositions are used in particular for washing and/or conditioning keratin materials such as the hair or the skin.