Context :

Aims : We study the dynamical status of the poor , low X–ray luminous galaxy clusters Abell 610 , Abell 725 , and Abell 796 ( at z = 0.1 , 0.09 , and 0.16 , respectively ) , containing diffuse radio sources ( relic , relic , and possible halo , respectively ) .

Methods : Our analysis is based on new spectroscopic data obtained at the William Herschel Telescope for 158 galaxies , new photometry obtained at the Isaac Newton Telescope with the addition of data recovered from the Data Release 5 of the Sloan Digital Sky Survey .
We use statistical tools to select 57 , 36 , and 26 cluster members and to analyze the kinematics of cluster galaxies , as well as to study the 2D cluster structure .

Results : The low values we compute for the global line–of–sight velocity dispersion of galaxies ( \sigma _ { V } = 420 - 700 km s ^ { -1 } ) confirm that these clusters are low–mass clusters .
Abell 610 shows a lot of evidence of substructure .
It seems to be formed by two structures separated by \sim 700 km s ^ { -1 } in the cluster rest–frame , having comparable \sigma _ { V } \sim 200 km s ^ { -1 } and likely causing a velocity gradient .
The velocity of the brightest cluster member ( BCMI ; a bright radio source ) is very close to the mean velocity of the higher velocity structure .
A third small , low–velocity group hosts the second brightest cluster member ( BCMII ) .
The analysis of the 2D galaxy distribution shows a bimodal distribution in the core elongated in the SE–NW direction and likely associated to BCMI and BCMII groups .
Abell 725 and Abell 796 , which are less sampled , show marginal evidence of substructure in the velocity space .
They are elongated in the 2D galaxy distribution .
For both Abell 610 and Abell 725 we shortly discuss the possible connection with the hosted diffuse radio relic .

Conclusions : Our results show that relic radio sources are likely connected with merger events , but are not limited to massive clusters .
About the possible halo source in Abell 796 , there is some evidence of a merger event in this non–massive cluster , but a pointed radio observation is necessary to confirm this halo .