A baby safety car seat (28) convertible into a rollable baby seat comprises a right and a left pair of front and rear legs (32, 34), a locking arrangement for the legs, and wheels (33, 35) with a special cut-out. The seat has an intermediate mode, in which a first one of the legs of each pair is in its operational position whilst the second leg of that pair is its intermediate position other than the storage and operational positions of this leg. The locking arrangement is configured for locking the first leg in its operational position to the seat's support portion whilst allowing the movement of the second leg between its intermediate and operational positions. Alternatively or in addition, when a first of the legs is in its operational position the second leg can be movable between its intermediate and operational position, and the locking mechanism can be configured for locking the front and rear legs of each pair to each other during their movement between their storage and intermediate states, and unlocking the legs from each other to allow the movement of the second leg between its intermediate and operational positions. The cut-out can be specifically oriented, can have specific proportions and can have a cut-out surface with a non-slip property and/or distinguishable color, or made of a material other than that, from which at least one other portion of the wheel's body is made.