A travelling control apparatus 1 includes: rotational speed ratio detection units 2 configured to output signals S1, S2 of respective rotational speeds of front and rear wheels; a rotational speed ratio calculation measure 3 for calculating data Da of a rotational speed ratio of the wheels from the signals S1, S2; a rotational speed ratio sort measure 4 for sorting the data Da into data D1 within a range of a set range T1 and data D2 out of the range; a reference data generation measure 5 for averaging the data D1 and generating an average value thereof as reference data Ds; and a slip determination measure 6 for comparing data Da1 of the rotational speed ratio of the wheels with the reference data Ds, and in a case of the data Da1 being out of a set range T2, for determining that one of the wheels is slipping.