Low-velocity aggregate-aggregate collisions play an important role for the developement of aggregate sizes during the first stages of accumulation of solid bodies in the preplanetary nebula. To study such collisions, an experimental setup was developed where two millimeter-sized dust aggregates collide in vacuum with relative velocities between ∼0.15 and ∼4 m sec-1. The impact parameters of the collisions are arbitrary so that central collisions as well as grazing collisions can be investigated. Two types of aggregates were used, (1) ZrSiO4 with constituent particle sizes ≤1 μm and 74% porosity and (2) Aerosil 200 (SiO2) with constituent particle sizes ∼12 nm and 97% porosity. The collision experiments were carried out in five narrow velocity windows in the above velocity regime for equal-sized aggregates (ZrSiO4(I), Aerosil 200) as well as for aggregates with a mean mass ratio of ∼66 (ZrSiO4(II)). Coagulation (i.e., sticking) of the aggregates was not observed. Low-velocity collisions resulted in restitution (i.e., bouncing), and at higher velocities, a transition from restitution to fragmentation was observed at ν ∼ 1 m sec-1 for ZrSiO4(I), as well as at ν ∼ 4 m sec-1 for Aerosil 200. For ZrSiO4(II), fragmentation at ν ∼ 4 m sec-1 was found in two cases only. Due to the lower transition velocity, the fragmentation of ZrSiO4(I) was investigated in more detail. The abundance of smaller fragments increases with increasing velocity and with decreasing impact parameter. At ν ∼ 4 m sec-1, the fragment numbers follow a power law mass distribution v (m)dm ∼ m-9/8dm. Extrapolation of the fragment mass distribution for catastrophic collisions between equal-sized aggregates were performed using a simple fragmentation model based on the following assumptions: (1) power law mass distribution between the constituent particle mass and the aggregate mass, (2) fragments have constant free surface energies per unit surface area, and (3) impact parameter-dependent efficiency for the transition of kinetic collision energy into free surface energy of the fragments. This model predicts a complete disintegration of the ZrSiO4(I) aggregates into their building blocks for collision velocities of ≥50 m sec-1. For aggregates consisting of van der Waals-bonded constituent particles of 0.1 μm radii, these catastrophic collision velocities are much smaller and are predicted to be ∼3 m sec-1. These are typical velocities for the preplanetary nebula, so catastrophic fragmentations could be frequent events if aggregates in the solar nebula formed due to weak surface forces.