A stroller apparatus can collapse in a compact and convenient manner. In some embodiments, the stroller apparatus can be provided with a mounting fixture capable of detachably fastening a child support accessory thereon. The mounting fixture affixed on the stroller frame can lock with a connector affixed on the child support accessory. The connector can be inserted into the mounting fixture for locking the child support accessory in position on the stroller frame. The connector can lock with the mounting fixture in either of a rearward and forward facing configuration of the child support accessory. In other embodiments, the stroller apparatus can include a child support that has a connector portion through which it is assembled with the stroller frame. The construction of the stroller frame is such that it can be conveniently collapsed in a compact form.