A complex manifold is (complete) hyperbolic if the Kobayashi pseudo-distance is a (complete) distance. In this note, it is shown that a fibre bundle is (complete) hyperbolic if both the base and fibre are (complete) hyperbolic. Two examples are also given. The first shows that the completion of a hyperbolic manifold is not necessarily locally compact. The second shows that one generalization of the big Picard theorem is false. In this note, we give an example of a hyperbolic manifold MV whose completion M* is not locally compact. It is also shown that a fibre bundle E is (complete) hyperbolic if both the base and fibre are (complete) hyperbolic. We begin by recalling the definition of the Kobayashi pseudodistance dm associated to the complex manifold M. Let p and q be points in M. By a chain a from p to q, we mean a sequence p =Po, Pl, * *, p= q of points in AM, points a1, * * *, ak in the unit disk D= {zECI zI <1} and holomorphic mapsfi, * , f' of D into M with fi(O) = pi-, and fi(ai) = pi. The length Ia I of a is defined by kc k 1-1Iai =E d(O, ai) E log i=l i=l 1 ai where d is the Poincare&Bergman distance on D. It is given by the metric ds2 -(1/(1 Iz 2)2)dzdz. We set dm(p, q) =-infaEA Ia , where A is the set of all chains fromi p to q. It is easy to see that dM is a pseudodistance on Mi. If dM is an actual distance, we say that M is hyperbolic. M is called comnplete hyperbolic if dml is a complete metric, i.e., if all Cauchy sequences converge. it follows immediately from the definition of dm and dv, that if f: Ml-N is holomorphic and p, qClI, thenl djr(J(p), f(q))