Damage in off-axis plies of composite laminates is studied by examining the configuration [0/±θ4/01/2]s with θ=25, 40, 55, 70 and 90 subjected to tensile loading in the axial direction. It is found that for the values of θ, where the stress in the off-axis plies normal to the fibers is tensile, ply cracks lying along fibers initiate and increase in number, while for other θ values the plies do not undergo this damage, as expected. However, the overall laminate elastic moduli are also found to change for the θ values where no ply cracks exist. It is postulated that a shear-induced degradation of the off-axis plies is responsible for the observed laminate moduli changes. The prediction of changes in these moduli by using the ply shear modulus measured on [±θ4]s appears to support this postulate. For the case of moduli changes caused by ply cracks the recently proposed synergistic damage-mechanics approach [1] is applied. The implications of the findings of this work on a class of continuum damage-mechanics formulations proposed in the literature are discussed.