We report on our on-going proper motion survey of very low-mass (>=5 MJup), ultracool (Teff>=350 K) companions of nearby, field T-type brown dwarfs in the Solar neighborhood. Our project is intended to provide seeing-limited images of the targets to find companion candidates at wide separations (>=15 AU) and within an area of 3'×3' around the primaries, thus complementing previous searches that explored the inner-most regions. Data are collected in the J-band with 2-4-m class telescopes; the completeness magnitude of our survey goes from ~19.5 to ~21 mag (depending on seeing and transparency conditions). So far we have studied 11 late-L and T-type brown dwarfs located at d<=16 pc of the Sun. Only one faint, proper motion companion candidate is found; its definitive confirmation highly requires third epoch data.