Abstract Optical microscopy, electron probe microanalysis, scanning electron microscopy and analytical transmission electron microscopy were used to study the interchondrule matrix and opaque chondrule rims in Bishunpur, Krymka, Semarkona, Chainpur (all LL3), Tieschitz and Sharps (both H3). The size-distribution of grains in matrix in Bishunpur obeys a power law. Rims around chondrules tend to be finer grained than matrix and may be layered. All rims and matrices studied contain clasts of forsteritic olivine and low-Ca pyroxene. In Bishunpur the clasts may be cemented by amorphous “glue”, rich in normative albite, and partly altered to smectite. Rims in Krymka, Sharps, Chainpur and Tieschitz have a densely packed olivine groundmass with a grain-size of about 0.1 μm. In Krymka, groundmass olivine is Fo 20–30 and forms interlocking dendrites. Various Fe oxides are present in rims and matrices. Grain-size distribution and chemical data indicate that clastic olivines and pyroxenes are derived from chondrules. From analyses, matrices/rims in the LL-group apparently are enriched in a feldspathic component. Tieschitz rims are slightly enriched, but here the feldspathic component is present as white matrix. Sharps rims are not enriched in a feldspathic component. Opaque interchondrule matrices and chondrule rims probably formed from the products of fragmentation of chondrules, partly induced by contraction of protopyroxene on inversion to clinopyroxene. Fragmented silica-rich chondrule mesostases reacted with Fe oxides and Na to form the groundmass of fayalitic olivine and feldspathic “glue”. A low-temperature, nebular or pre-solar, component is limited to 3 vol.% of each meteorite, so equilibrium condensate was not the carrier of volatiles such as Tl and Bi.