[3] The following genera and species are assigned to the family:[3] Viruses in the genus Tristromaviridae are enveloped, with rod-shaped geometries.

MCP1 and MCP2 form a heterodimer, which wraps around the linear dsDNA genome transforming it into A-form.

[6] The helical nucleocapsid is surrounded by a lipid envelope and contains other viral proteins, with VP3 being the most abundant.

[7] The fold of the MCPs as well as virions organization of tristromaviruses are similar to those of members of the families Rudiviridae[8] and Lipothrixviridae,[9][10] which together constitute the order Ligamenvirales.

Due to these structural similarities, order Ligamenvirales and family Tristromaviridae were proposed to be unified within a class 'Tokiviricetes' (toki means ‘thread’ in Georgian and viricetes is an official suffix for a virus class).