1. Every family of subnormal operators in a Hilbert space fulfils the Halmos-Bram condition on a suitable dense subset of its domain , . In  and  it is shown that the generalized commutation relation implies the Halmos-Bram condition for one operator. In this paper it is proved that the generalized commutation relation implies the Halmos-Bram condition for infinite families of operators (in a special case Jorgensen proved it in a different way for finite families of operators, see ) and as an example of the application of this property it is shown that every family of generalized creation operators in the Bargmann space of an infinite order, indexed by mutually orthogonal vectors from I2 is subnormal. See  for the definitions.