The protons which repeal each other electrostatically & the neutron which exert no electric force are held extremely close together inside a stable nucleus.
Obviously there are some forces operating within the nucleus which binds neutron to proton (n-p forces), proton to protons ( p-p forces) and neutron to neutron (n-n forces). These forces bind the nucleus.
Nuclear forces has following properties :
i) They are attractive : The overall effect of Nuclear forces is attractive otherwise the nucleus will not exist.
ii) They are non electric : The nuclear forces cannot be of electrical nature. If it will so, the protons will repel one another.
iii) They are non gravitational.
iv) They are extremely strong : The nuclear forces are strongest known forces in nature. Therefore they provide stability to nucleus.
v) They are extremely short range forces : These forces are applicable only in a small region of order of 10^-15 m. These forces donot obey inverse square law.
vi) They are spin dependent : Experimental evidences shows that the nuclear force acting between two nucleons depends upon the mutual orientation of spins of nucleons. e.g. a neutron and a proton are kept together forming a deutron only if their spins are parallel to each other.