We study the orbits of the various types of galaxies observed in the ESO Nearby Abell Cluster Survey . We combine the observed kinematics and projected distributions of galaxies of various types with an estimate of the mass density profile of the ensemble cluster to derive velocity-anisotropy profiles . Galaxies within and outside substructures are considered separately . Among the galaxies outside substructures we distinguish four classes , on the basis of their projected phase-space distributions . These classes are : the brightest ellipticals ( with M _ { R } \leq - 22 + 5 \log h ) , the other ellipticals together with the S0 ’ s , the early-type spirals ( Sa–Sb ) , and the late-type spirals and irregulars ( Sbc-Irr ) together with the emission-line galaxies ( except those of early morphology ) . The mass profile was determined from the distribution and kinematics of the early-type ( i.e . elliptical and S0 ) galaxies outside substructures ; the latter were assumed to be on isotropic orbits , which is supported by the shape of their velocity distribution . The projected distribution and kinematics of the galaxies of other types are used to search for equilibrium solutions in the gravitational potential derived from the early-type galaxies . We apply the method described by Binney & Mamon as implemented by Solanes & Salvador-Solé to derive , to our knowledge for the first time , the velocity anisotropy profiles of all galaxy classes individually ( except , of course , the early-type class ) . We check the validity of the solutions for \beta ^ { \prime } ( r ) \equiv [ { < v _ { r } ^ { 2 } > ( r ) } / { < v _ { t } ^ { 2 } > ( r ) } ] % ^ { 1 / 2 } , where < v _ { r } ^ { 2 } > ( r ) and < v _ { t } ^ { 2 } > ( r ) are the mean squared components of the radial and tangential velocity , respectively , by comparing the observed and predicted velocity-dispersion profiles . For the brightest ellipticals we are not able to construct equilibrium solutions . This is most likely the result of the formation history and the special location of these galaxies at the centres of their clusters . For both the early and the late spirals , as well as for the galaxies in substructures , the data allow equilibrium solutions . The data for the early spirals are consistent with isotropic orbits ( \beta ^ { \prime } ( r ) \equiv 1 ) , although there is an apparent radial anisotropy at \simeq 0.45 r _ { 200 } . For the late spirals an equilibrium solution with isotropic orbits is rejected by the data at the > 99 % confidence level . While \beta ^ { \prime } ( r ) \approx 1 within 0.7 r _ { 200 } , \beta ^ { \prime } increases linearly with radius to a value \simeq 1.8 at 1.5 r _ { 200 } . Taken at face value , the data for the galaxies in substructures indicate that isotropic solutions are not acceptable , and tangential orbits are indicated . Even though the details of the tangential anisotropy remain to be determined , the general conclusion appears robust . We briefly discuss the possible implications of these velocity-anisotropy profiles for current ideas of the evolution and transformation of galaxies in clusters .